The equation y = - 8) is graphed in the zy-plane. Which of the following equations will have a graph that is parallel to the graph of the above equation and have an X-intercept on the
negative x-axis?

Explanation:

Given

Required

Equation of line with the same slope and x intercept on negative axis

We start by solving for the slope of the first equation.

It should be noted that the slope of a line (in equation form) is the coefficient of x.

So, we start by opening the bracket of

This gives

Hence, the slope of the line is

To solve for x intercept, we simply substitute 0 for y. This gives.

Add 12 to both sides

Multiply both sides by ⅔

This is the x intercept of equation

From the question we understand that the second equation has the same slope and has a negative x intercept as

For two parallel lines, their slope are always equal.

Hence, the second equation has the following info.

This can be rewritten as follows;.

x = -8

Add 8 to both sides

x + 8 = -8 + 8

x + 8 = 0

Multiply both sides by the slope (3/2)

Recall that to solve for x intercept, we simply substitute 0 for y.

At this point, we also replace 0 with y.

This gives

Hence, the equation of the second line is