Question

What is the equation of the line that is parallel to the given line and has an x-intercept of –3?

Answer 1

You did not include the given line to which your line is parallel to.

Nevertheless, I can explain you how to solve this problem and which the possible solutions are.

1) x-intercept = - 3 = y = 0

The only two equations that include the point (-3,0) are y = x + 3 and y = - x - 3 (you likely forgot to place the negative signs).

You can prove that in this way:

a) y = x + 3
y = 0 => x + 3 = 0 => x = - 3

b) y = - x - 3
y = 0 => - x - 3 = 0 => x = - 3

Then, so far you have two options: y = x + 3 and y = - x - 3.

2) The slope of y = x + 3 is 1 and the slope of y = - x - 3 = - 1 (the coefficient of the x).

3) You know that line whose equation you are determining is parallel to the given line. That means that their slope are the same. So, your next step is to determine the slope of the given line. It shall be either 1 or - 1. Once you have the slope, you will know whether the solution is y = x + 3 or y = - x - 3.