Question

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

Answer 1

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

Answer 2

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)\; =\; (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=(8-2)/(-4-0)=(6)/(-4) =(-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=(12-6x)/(4)=(12)/(4) -(6x)/(4) =-(6)/(4)x+3`

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

`-4y=6x+4\\ \\ (-4y)/(-4)=(6x)/(-4)+(4)/(-4) \\ \\ y=(-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

`(2y)/(2) =(-3x)/(2)+(5)/(2) \\ \\ y=(-3)/(2) x+(5)/(2)`