Write an Equation and Then Solve It Art Specific Pionts

Graphs

33 Graph Linear Equations in Two Variables

Learning Objectives

By the cease of this section, y'all will be able to:

Recognize the human relationship between the solutions of an equation and its graph.
Graph a linear equation by plotting points.
Graph vertical and horizontal lines.

Recognize the Relationship Between the Solutions of an Equation and its Graph

In the previous section, we found several solutions to the equation $3x+2y=6$ . They are listed in (Figure). And then, the ordered pairs $\left(0,3\right)$ , $\left(2,0\right)$ , and $\left(1,\frac{3}{2}\right)$ are some solutions to the equation $3x+2y=6$ . We tin plot these solutions in the rectangular coordinate organisation as shown in (Figure).

$3x+2y=6$
$x$	$y$	$\left(x,y\right)$
0	three	$\left(0,3\right)$
two	0	$\left(2,0\right)$
i	$\frac{3}{2}$	$\left(1,\frac{3}{2}\right)$

The figure shows four points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the four points at (0, 3), (1, three halves), (2, 0), and (4, negative 3). The four points appear to line up along a straight line.

Notice how the points line up perfectly? We connect the points with a line to get the graph of the equation $3x+2y=6$ . See (Figure). Notice the arrows on the ends of each side of the line. These arrows signal the line continues.

Every point on the line is a solution of the equation. Also, every solution of this equation is a bespeak on this line. Points non on the line are not solutions.

Observe that the bespeak whose coordinates are $\left(-2,6\right)$ is on the line shown in (Effigy). If yous substitute $x=-2$ and $y=6$ into the equation, you find that it is a solution to the equation.

The figure shows a straight line and two points and on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the two points and are labeled by the coordinates

The figure shows a series of equations to check if the ordered pair (negative 2, 6) is a solution to the equation 3x plus 2y equals 6. The first line states

So the point $\left(-2,6\right)$ is a solution to the equation $3x+2y=6$ . (The phrase "the betoken whose coordinates are $\left(-2,6\right)$ " is often shortened to "the point $\left(-2,6\right)$ .")

The figure shows a series of equations to check if the ordered pair (4, 1) is a solution to the equation 3x plus 2y equals 6. The first line states

And so $\left(4,1\right)$ is not a solution to the equation $3x+2y=6$ . Therefore, the betoken $\left(4,1\right)$ is not on the line. Run across (Effigy). This is an example of the saying, "A picture is worth a grand words." The line shows you all the solutions to the equation. Every point on the line is a solution of the equation. And, every solution of this equation is on this line. This line is called the graph of the equation $3x+2y=6$ .

Graph of a Linear Equation

The graph of a linear equation $Ax+By=C$ is a line.

Every point on the line is a solution of the equation.
Every solution of this equation is a point on this line.

The graph of $y=2x-3$ is shown.

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line has a positive slope and goes through the y-axis at the (0, negative 3). The line is labeled with the equation y equals 2x negative 3.

For each ordered pair, make up one's mind:

ⓐ Is the ordered pair a solution to the equation?
ⓑ Is the point on the line?

A $\left(0,-3\right)$ B $\left(3,3\right)$ C $\left(2,-3\right)$ D $\left(-1,-5\right)$

Utilize the graph of $y=3x-1$ to determine whether each ordered pair is:

a solution to the equation.
on the line.

ⓐ $\left(0,-1\right)$ ⓑ $\left(2,5\right)$

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the point (negative 2, negative 7) and for every 3 units it goes up, it goes one unit to the right. The line is labeled with the equation y equals 3x minus 1.

ⓐ yeah, yesⓑ aye, yeah

Use graph of $y=3x-1$ to decide whether each ordered pair is:

a solution to the equation
on the line

ⓐ $\left(3,-1\right)$ ⓑ $\left(-1,-4\right)$

ⓐ no, noⓑ aye, yep

Graph a Linear Equation by Plotting Points

There are several methods that can be used to graph a linear equation. The method nosotros used to graph $3x+2y=6$ is chosen plotting points, or the Point–Plotting Method.

How To Graph an Equation By Plotting Points

Graph the equation $y=2x+1$ past plotting points.

Graph the equation by plotting points: $y=2x-3$ .

Graph the equation by plotting points: $y=-2x+4$ .

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), (4, negative 4), and (5, negative 6). There are arrows at the ends of the line pointing to the outside of the figure.

The steps to take when graphing a linear equation by plotting points are summarized beneath.

Graph a linear equation by plotting points.

Find 3 points whose coordinates are solutions to the equation. Organize them in a table.
Plot the points in a rectangular coordinate arrangement. Check that the points line upwards. If they do not, carefully check your work.
Draw the line through the 3 points. Extend the line to make full the grid and put arrows on both ends of the line.

Information technology is true that information technology merely takes two points to determine a line, but it is a good habit to use iii points. If yous only plot two points and one of them is incorrect, you tin can still describe a line but it will not represent the solutions to the equation. It will be the wrong line.

If you use three points, and one is incorrect, the points will non line up. This tells you something is wrong and you demand to check your work. Look at the difference betwixt part (a) and part (b) in (Figure).

Figure a shows three points with a straight line going through them. Figure b shows three points that do not lie on the same line.

Let's do some other instance. This fourth dimension, nosotros'll show the concluding two steps all on one grid.

Graph the equation $y=-3x$ .

Solution

Notice iii points that are solutions to the equation. Here, again, it's easier to choose values for $x$ . Do yous see why?

We list the points in (Figure).

$y=-3x$
$x$	$y$	$\left(x,y\right)$
0	0	$\left(0,0\right)$
ane	$-3$	$\left(1,-3\right)$
$-2$	6	$\left(-2,6\right)$

Plot the points, bank check that they line up, and draw the line.

Graph the equation past plotting points: $y=-4x$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 2, 8), (0, 0), and (2, negative 8). The line has arrows on both ends pointing to the outside of the figure.

Graph the equation by plotting points: $y=x$ .

When an equation includes a fraction as the coefficient of $x$ , nosotros can all the same substitute any numbers for $x$ . But the math is easier if we make 'skillful' choices for the values of $x$ . This fashion nosotros volition avert fraction answers, which are hard to graph precisely.

Graph the equation $y=\frac{1}{2}x+3$ .

Graph the equation $y=\frac{1}{3}x-1$ .

Graph the equation $y=\frac{1}{4}x+2$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 12, negative 1), (negative 8, 0), (negative 4, 1), (0, 2), (4, 3), (8, 4), and (12, 5). The line has arrows on both ends pointing to the outside of the figure.

So far, all the equations we graphed had $y$ given in terms of $x$ . Now we'll graph an equation with $x$ and $y$ on the same side. Let's run into what happens in the equation $2x+y=3$ . If $y=0$ what is the value of $x$ ?

This bespeak has a fraction for the x– coordinate and, while nosotros could graph this bespeak, information technology is hard to be precise graphing fractions. Recollect in the instance $y=\frac{1}{2}x+3$ , we carefully chose values for $x$ and so as not to graph fractions at all. If nosotros solve the equation $2x+y=3$ for $y$ , information technology will be easier to find three solutions to the equation.

$\begin{array}{ccc}\hfill 2x+y& =\hfill & 3\hfill \\ \hfill y& =\hfill & -2x+3\hfill \end{array}$

The solutions for $x=0$ , $x=1$ , and $x=-1$ are shown in the (Figure). The graph is shown in (Figure).

$2x+y=3$
$x$	$y$	$\left(x,y\right)$
0	3	$\left(0,3\right)$
1	1	$\left(1,1\right)$
$-1$	v	$\left(-1,5\right)$

Tin can you locate the signal $\left(\frac{3}{2},0\right)$ , which we found by letting $y=0$ , on the line?

Graph the equation $3x+y=-1$ .

Graph the equation $2x+y=2$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 2, 6), (0, 2), (2, negative 2), (4, negative 6), and (6, negative 10). The line has arrows on both ends pointing to the outside of the figure.

Graph the equation $4x+y=-3$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, 9), (negative 2, 5), (negative 1, 1), (0, negative 3), (1, negative 7), and (2, negative 10). The line has arrows on both ends pointing to the outside of the figure.

If you can choose whatsoever three points to graph a line, how will you know if your graph matches the one shown in the answers in the book? If the points where the graphs cross the x– and y-axis are the same, the graphs match!

The equation in (Figure) was written in standard class, with both $x$ and $y$ on the same side. Nosotros solved that equation for $y$ in just one step. Just for other equations in standard form it is not that easy to solve for $y$ , so we will leave them in standard form. We tin can yet find a offset point to plot past letting $x=0$ and solving for $y$ . We tin can plot a second point by letting $y=0$ and and then solving for $x$ . Then nosotros will plot a 3rd point by using some other value for $x$ or $y$ .

Graph the equation $2x-3y=6$ .

Graph the equation $4x+2y=8$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), and (4, negative 4). The line has arrows on both ends pointing to the outside of the figure.

Graph the equation $2x-4y=8$ .

Graph Vertical and Horizontal Lines

Tin can we graph an equation with only one variable? Merely $x$ and no $y$ , or just $y$ without an $x$ ? How will nosotros make a table of values to go the points to plot?

Allow'due south consider the equation $x=-3$ . This equation has but one variable, $x$ . The equation says that $x$ is always equal to $-3$ , then its value does non depend on $y$ . No thing what $y$ is, the value of $x$ is e'er $-3$ .

And then to make a table of values, write $-3$ in for all the $x$ values. And then cull any values for $y$ . Since $x$ does non depend on $y$ , you can choose whatever numbers you similar. Only to fit the points on our coordinate graph, we'll use 1, 2, and 3 for the y-coordinates. Run into (Effigy).

$x=-3$
$x$	$y$	$\left(x,y\right)$
$-3$	i	$\left(-3,1\right)$
$-3$	ii	$\left(-3,2\right)$
$-3$	3	$\left(-3,3\right)$

Plot the points from (Figure) and connect them with a straight line. Notice in (Effigy) that we accept graphed a vertical line.

Vertical Line

A vertical line is the graph of an equation of the form $x=a$ .

The line passes through the x-centrality at $\left(a,0\right)$ .

Graph the equation $x=2$ .

Graph the equation $x=5$ .

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (5, 1), (5, 2), (5, 3), and all other points with first coordinate 5. The line has arrows on both ends pointing to the outside of the figure.

Graph the equation $x=-2$ .

What if the equation has $y$ but no $x$ ? Let's graph the equation $y=4$ . This fourth dimension the y– value is a constant, so in this equation, $y$ does not depend on $x$ . Fill in four for all the $y$ 's in (Effigy) and then choose whatever values for $x$ . We'll use 0, 2, and 4 for the x-coordinates.

$y=4$
$x$	$y$	$\left(x,y\right)$
0	4	$\left(0,4\right)$
two	4	$\left(2,4\right)$
4	4	$\left(4,4\right)$

The graph is a horizontal line passing through the y-axis at iv. See (Figure).

Horizontal Line

A horizontal line is the graph of an equation of the form $y=b$ .

The line passes through the y-axis at $\left(0,b\right)$ .

Graph the equation $y=-1.$

Graph the equation $y=-4$ .

Graph the equation $y=3$ .

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 3), (0, 3), (4, 3), and all other points with second coordinate 3. The line has arrows on both ends pointing to the outside of the figure.

The equations for vertical and horizontal lines expect very similar to equations like $y=4x.$ What is the divergence betwixt the equations $y=4x$ and $y=4$ ?

The equation $y=4x$ has both $x$ and $y$ . The value of $y$ depends on the value of $x$ . The y-coordinate changes according to the value of $x$ . The equation $y=4$ has simply one variable. The value of $y$ is constant. The y-coordinate is always 4. It does not depend on the value of $x$ . Come across (Figure).

$y=4x$			$y=4$
$x$	$y$	$\left(x,y\right)$	$x$	$y$	$\left(x,y\right)$
0	0	$\left(0,0\right)$	0	4	$\left(0,4\right)$
1	4	$\left(1,4\right)$	1	4	$\left(1,4\right)$
2	8	$\left(2,8\right)$	2	four	$\left(2,4\right)$

The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. One line is a straight horizontal line labeled with the equation y equals 4. The other line is a slanted line labeled with the equation y equals 4x.

Find, in (Figure), the equation $y=4x$ gives a slanted line, while $y=4$ gives a horizontal line.

Graph $y=-3x$ and $y=-3$ in the same rectangular coordinate system.

Graph $y=-4x$ and $y=-4$ in the aforementioned rectangular coordinate system.

Graph $y=3$ and $y=3x$ in the same rectangular coordinate system.

Central Concepts

Graph a Linear Equation past Plotting Points
1. Find three points whose coordinates are solutions to the equation. Organize them in a table.
2. Plot the points in a rectangular coordinate organization. Check that the points line upward. If they do not, carefully check your work!
3. Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.

Practice Makes Perfect

Recognize the Relationship Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, decide:

ⓐ Is the ordered pair a solution to the equation?ⓑ Is the indicate on the line?

ⓐ yes; noⓑ no; noⓒ yes; yepⓓ yeah; aye

ⓐ yes; yesⓑ yes; ayeⓒ yeah; yesⓓ no; no

Graph a Linear Equation by Plotting Points

In the following exercises, graph past plotting points.

$y=3x-1$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 10), (negative 2, negative 7), (negative 1, negative 4), (0, negative 1), (1, 2), (2, 5), and (3, 8).

$y=2x+3$

$y=-2x+2$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 3, 8), (negative 2, 6), (negative 1, 4), (0, 2), (1, 0), (2, negative 2), (3, negative 4), (4, negative 6), and (5, negative 8).

$y=-3x+1$

$y=x+2$

$y=x-3$

$y=\text{−}x-3$

$y=\text{−}x-2$

$y=2x$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 5, negative 10), (negative 4, negative 8), (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10).

$y=3x$

$y=-4x$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, 12), (negative 2, 8), (negative 1, 4), (0, 0), (1, negative 4), (2, negative 8), and (3, negative 12).

$y=-2x$

$y=\frac{1}{2}x+2$

$y=\frac{1}{3}x-1$

$y=\frac{4}{3}x-5$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 9), (0, negative 5), (3, negative 1), (6, 3), and (9, 7).

$y=\frac{3}{2}x-3$

$y=-\frac{2}{5}x+1$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 5), (negative 5, 3), (0, 1), (5, negative 1), and (10, negative 3).

$y=-\frac{4}{5}x-1$

$y=-\frac{3}{2}x+2$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 6, 11), (negative 4, 8), (negative 2, 5), (0, 2), (2, negative 1), (4, negative 4), (6, negative 7), and (8, negative 10).

$y=-\frac{5}{3}x+4$

$x+y=6$

$x+y=4$

$x+y=-3$

$x+y=-2$

$x-y=2$

$x-y=1$

$x-y=-1$

$x-y=-3$

$3x+y=7$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to -7. The equation 3 x plus y equals 7 is graphed.

$5x+y=6$

$2x+y=-3$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 5, 7), (negative 4, 5), (negative 3, 3), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 5), and (2, negative 7).

$4x+y=-5$

$\frac{1}{3}x+y=2$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 4), (negative 3, 3), (0, 2), (3, 1), and (6, 0).

$\frac{1}{2}x+y=3$

$\frac{2}{5}x-y=4$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 5, negative 2), (0, negative 4), and (5, negative 6).

$\frac{3}{4}x-y=6$

$2x+3y=12$

$4x+2y=12$

$3x-4y=12$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 4, negative 6), (0, negative 3), (4, 0), and (8, 3).

$2x-5y=10$

$x-6y=3$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative three halves), (negative 3, negative 1), (0, negative one half), (3, 0), and (6, one half).

$x-4y=2$

$5x+2y=4$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, 7), (0, 2), (2, negative 3), and (4, negative 8).

$3x+5y=5$

Graph Vertical and Horizontal Lines

In the following exercises, graph each equation.

$x=4$

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (4, 0), (4, 1), (4, 2) and all points with first coordinate 4.

$x=3$

$x=-2$

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (negative 2, 0), (negative 2, 1), (negative 2, 2) and all points with first coordinate negative 2.

$x=-5$

$y=3$

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, 3), (1, 3), (2, 3) and all points with second coordinate 3.

$y=1$

$y=-5$

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, negative 5), (1, negative 5), (2, negative 5) and all points with second coordinate negative 5.

$y=-2$

$x=\frac{7}{3}$

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (7/3, 0), (7/3, 1), (7/3, 2) and all points with first coordinate 7/3.

$x=\frac{5}{4}$

$y=-\frac{15}{4}$

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 15/4), (1, negative 15/4), (2, negative 15/4) and all points with second coordinate negative 15/4.

$y=-\frac{5}{3}$

In the following exercises, graph each pair of equations in the aforementioned rectangular coordinate system.

$y=5x$ and $y=5$

$y=-\frac{1}{3}x$ and $y=-\frac{1}{3}$

Mixed Exercise

In the following exercises, graph each equation.

$y=4x$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, negative 8), (negative 1, negative 4), (0, 0), (1, 4), and (2, 8).

$y=2x$

$y=-\frac{1}{2}x+3$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 6), (negative 4, 5), (negative 2, 4), (0, 3), (2, 2), (4, 1), and (6, 0).

$y=\frac{1}{4}x-2$

$y=\text{−}x$

$y=x$

$x-y=3$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 3, negative 7), (negative 2, negative 6), (negative 1, negative 4), (0, negative 3), (1, negative 2), (2, negative 1), (3, 0), (4, 1), (5, 2), and (6, 3).

$x+y=-5$

$4x+y=2$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, 6), (negative 1, 4), (0, 2), (1, negative 2), and (2, negative 6).

$2x+y=6$

$y=-1$

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 1), (1, negative 1), (2, negative 1) and all points with second coordinate negative 1.

$y=5$

$2x+6y=12$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 4), (negative 3, 3), (0, 2), (3, 1), and (6, 0).

$5x+2y=10$

$x=3$

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The vertical line goes through the points (3, 0), (3, 1), (3, 2) and all points with first coordinate 3.

$x=-4$

Everyday Math

Motor home toll. The Robinsons rented a motor home for one calendar week to go on holiday. It cost them ?594 plus ?0.32 per mile to rent the motor dwelling, then the linear equation $y=594+0.32x$ gives the cost, $y$ , for driving $x$ miles. Calculate the rental toll for driving 400, 800, and 1200 miles, so graph the line.

?722, ?850, ?978

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from 0 to 1200 in increments of 100. The y-axis of the plane runs from 0 to 1000 in increments of 100. The straight line starts at the point (0, 594) and goes through the points (400, 722), (800, 850), and (1200, 978). The right end of the line has an arrow pointing up and to the right.

Writing Exercises

Explicate how you lot would choose 3 x– values to brand a tabular array to graph the line $y=\frac{1}{5}x-2$ .

Answers will vary.

What is the difference between the equations of a vertical and a horizontal line?

Self Bank check

ⓐ Afterward completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has 4 rows and 4 columns. The first row is a header row and it labels each column. The first column header is

ⓑ After reviewing this checklist, what will you lot exercise to get confident for all goals?

phillipsthatimbers.blogspot.com

Source: https://opentextbc.ca/elementaryalgebraopenstax/chapter/graph-linear-equations-in-two-variables/

Write an Equation and Then Solve It Art Specific Pionts

33 Graph Linear Equations in Two Variables

Learning Objectives

Recognize the Relationship Between the Solutions of an Equation and its Graph

Graph a Linear Equation by Plotting Points

Graph Vertical and Horizontal Lines

Central Concepts

Practice Makes Perfect

Mixed Exercise

Everyday Math

Writing Exercises

Self Bank check

0 Response to "Write an Equation and Then Solve It Art Specific Pionts"

Post a Comment

Iklan Atas Artikel

Iklan Tengah Artikel 1

Iklan Tengah Artikel 2

Iklan Bawah Artikel