Question

Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations? (5 points)

4x + 2y = −2
x − 3y = 24

Options for answer:

The slopes are different, and the y-intercepts are different.
The slopes are different, and the y-intercepts are the same.
The slopes are the same, and the y-intercepts are different.
The slopes are the same, and the y-intercepts are the same.

Answer 1

The slopes are different, and the y-intercepts are different.

Explanation:

First, slove for slope-intercept form (y=mx+b)

for the first one, subtract 4x from both sides' 4x-4x+2y=-2-4x

Then, divide both sides by 2; which gets you y=-1-2x. we can re-write that as y=-2x-1.

The slope is -2, and the y-inter. is -1.

For the second one, we subtract x from both sides, leaving us with -3y=-x+24. We divide both sides by -3, which gets us y=-1/3x-8.

The slope is -1/3, and the y-inter. is -8.