Question

Consider the system of equations shown below.

Answer 1

Answer:

The linear equations have the same slope but different y-intercepts.

Step-by-step explanation:

A linear equation has the general form

$y=mx+b$

where $m$ is the slope and $b$ is the y-intercept.

In the case of the first line $y=-5x+1$

$m=-5$

and $b=1$

for the second line $y=-5x+10$

$m=-5$

and $b=10$

Thus, the lines have the same slope but a different y-intercept.

This is why they are parallel, because they increase at the same rate always (hence the same slope) and the cross the y-axis at different point (hence the different y-intecept)

Answer 2

The linear equations have the same slope but different y-intercepts. This is the right answer because you can see the x coefficient for both equations is -5 but 1 and 10 are not the same and they are y-intercepts. These two are parallel so they will never meet.