Chapter 5.6, Problem 1STP

For Exercises $1-5,$ choose the correct letter.

Which equation has a graph parallel to the graph of $9x+3y=-22?$

A. $y=3x-22$

B. $y=-3x+8$

C. $y=\frac{1}{3}x+12$

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

To determine

To find: The equation that has a graph parallel to the graph of $9x+3y=-22$ .

Answer to Problem 1STP

The equation that has a graph parallel to the graph of $9x+3y=-22$ is given in option B.

Explanation of Solution

Given information:

The options given are

  

To determine the equation that has a graph parallel to the graph of $9x+3y=-22$ , express the equation in slope-intercept form as follows:

  $\begin{array}{l}9x+3y=-22\\ \Rightarrow 3y=-9x-22\\ \Rightarrow y=-\frac{9}{3}x-\frac{22}{3}\\ \Rightarrow y=-3x-\frac{22}{3}\end{array}$

Here, the slope of the line is $-3$ . So to find the equation that has a graph parallel to the graph of $9x+3y=-22$ , we need to look for the equation that has the same slope $-3$ .

Conclusion:

Among the given equations, the only equation that has the same slope $-3$ is $y=-3x+8$ . Therefore, the equation that has a graph parallel to the graph of $9x+3y=-22$ is given in option B.