Question

On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3).
What is the equation of the line that is parallel to the given line and passes through the point (2, 3)?

x + 2y = 4
x + 2y = 8
2x + y = 4
2x + y = 8

Answer 1

Slope = (-4 - 0)/(4 - (-4)) = -4/8 = -1/2.
Line through (2,3) with slope -1/2: y = (-1/2)x + b, 3 = (-1/2)(2) + b → 3 = -1 + b → b = 4.
So y = (-1/2)x + 4 → multiply by 2: x + 2y = 8.

Answer: x + 2y = 8