Question

On a coordinate plane, a line with positive slope goes through points (negative 6, negative 4) and (0, 6). A point is at (4, negative 6).
Use the given line and the point not on the line to answer the question.

What is the point on the line perpendicular to the given line, passing through the given point that is also on the y-axis?

(−3.6, 0)
(−2, 0)
(0, −3.6)
(0, −2)

Answer 1

Slope of given line = (6 − (−4)) / (0 − (−6)) = 10/6 = 5/3.
Perpendicular slope = −3/5.
Line through (4, −6): y + 6 = (−3/5)(x − 4) ⇒ y = (−3/5)x − 18/5 = (−3/5)x − 3.6.
At x = 0 (y‑axis): y = −3.6.

Answer: (0, −3.6).