Question

"Identify the pair of equations that represent a line that is parallel to the line x=−4 and a line that is perpendicular to the line x=−4. Write an equation in standard form of the line shown.

A. x=y−4 and y=−4
B. x=y/-4 and y=4
C. x=4 and y=4
D. x=−1/4 and y=2x"

Answer 1

The correct pair of equations is Choice C: x=4 and y=4. The line x=-4 is vertical, so a parallel line must also be vertical, and a perpendicular line to a vertical line is a horizontal line.

Step-by-step explanation:

The question asks us to identify a pair of equations with one that is parallel to the line x=-4 and another that is perpendicular to the line x=-4. The line x=-4 is a vertical line, thus any line that is parallel to it would also have to be a vertical line. This means the equation for the parallel line would not involve y and would have the form x=constant. The perpendicular line to a vertical line is a horizontal line, which would have the form y=constant. So we need to find equations with these forms.

Looking at the choices given:

Therefore, the correct answer is Choice C: x=4 and y=4.