Question

Which equations have the same slope as the graph above? Select all that apply.

Answer 1

Given:

The graph given passes through two points (0, 2) and (-4, 8).

General Idea:

We can find the slope (m) of a line passing through two points say A and B using the below formula.

$A(x_1,y_1) \; and \; B(x_2,y_2) \; the\; two\; points\\ \\ Slope\; (m)\; =\; \frac{y_2-y_1}{x_2-x_1}$

Applying the concept:

Slope of the line given using the two points (0, 2) and (-4, 8).

$m=\frac{8-2}{-4-0}=\frac{6}{-4} =\frac{-3}{2}$

Out of the five options given , we need to check which options have slope as -6/4 or -3/2 by rewriting (if needed) the given to slope intercept form y =mx + b and compare the same.

Conclusion:

Rewriting the first option, the slope is -6/4 as shown below.

$y=\frac{12-6x}{4}=\frac{12}{4} -\frac{6x}{4} =-\frac{6}{4}x+3$

Rewriting the fourth option, the slope is -3/2 as show below.

$-4y=6x+4\\ \\ \frac{-4y}{-4}=\frac{6x}{-4}+\frac{4}{-4} \\ \\ y=\frac{-3}{2}x-1$

Rewriting the fifth option, the slope is -3/2 as shown below.

$2y+3x-5=0\\Subtract \; 3x\; and\; add\; 5\; on\; both\; sides\; of\; the\; equation\\ \\ 2y+3x-5-3x+5=0-3x+5\\ Combine\; like\; terms\\\\ 2y=-3x+5$

Divide by 2 throughout the equation

$\frac{2y}{2} =\frac{-3x}{2}+\frac{5}{2} \\ \\ y=\frac{-3}{2} x+\frac{5}{2}$

Answer 2

A, D, and E have the same slope as the graph shown. the reason why is that they all have a slope of -3/2