Question

On a coordinate plane, a line goes through (negative 3, negative 4) and (3, 0).
What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?

The slope is Negative three-halves and contains the point (0, 2).
The slope is Negative two-thirds and contains the point (0, −2).
The slope is Three-halves and contains the point (0, 2).
The slope is Negative three-halves and contains the point (0, −2).

Answer 1

First find the original line's slope and y-intercept.
Slope = (0 − (−4)) / (3 − (−3)) = 4/6 = 2/3.
Using (3,0): 0 = (2/3)(3) + b ⇒ b = −2. So the line is y = (2/3)x − 2.

A perpendicular line has slope = negative reciprocal = −3/2, and the same y-intercept is (0, −2).

So the correct choice is: "The slope is Negative three-halves and contains the point (0, −2)."