Question

Given the following system of equations and their graph below, what can be determined about the slopes and y-intercepts of the system of equations?

(Graph)
4x + 2y = −2
x − 3y = 24

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:

From the graph:

Parallel lines have the same slope.

The lines are not parallel, therefore have the different slopes.

y-intercepts are different (look at the picture)

-1 and -8.

Answer:

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

From the system of equations:

The slope-ntercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

We have the equations of a lines in the standard form (Ax + By = C).

Convert ot the slope-intercept form:

`4x+2y=-2` subtract 4x from both sides

`2y=-4x-2` divide both sides by 2

`y=-2x-1`

Therefore we have the slope m = -2, and the y-intercept b = -1.

`x-3y=24` subtract x from both sides

`-3y=-x+24` divide both sides by (-3)

`y=(1)/(3)x-8`

Therefore we have the slope m = 1/3, and the y-intercept b = -8.

-2 ≠ 1/3 and -1 ≠ -8

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

Answer 2

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

Explanation:

The lines on the graph are not parallel, so the slopes are different.

The lines on the graph intersect the y-axis in different places, so the y-intercepts are different.