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?

A line includes points 0 comma 4 and 2 comma 3. A line includes points 0 comma 3 and 4 comma 1. x + 2y = 8
2x + 4y = 12
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 the same, and the y-intercepts are different

Explanation:

To find the slope of each equation, we first need to rewrite the equations isolating y. So, we have that:

First equation:

x + 2y = 8

2y = 8 - x

y = -0.5x + 4

Second equation:

2x + 4y = 12

x + 2y = 6

2y = 6 - x

y = -0.5x + 3

The slope is the coefficient of x, and they are the same in both equations, so they have the same slope.

The y-intercepts is the constant that is not multiplied by x, so in the first equation it is 4, and in the second it is 3, so the equations don't have the same y-intercepts.