Question

Lines A and B are perpendicular and have the same x-intercept. The equation of line A
is x + 2y - 4 = 0 . Determine the y-intercept of line B.

A.-8
B.-2
C. 4
D. 8

This is the work that I did:

x + 2y - 4 = 0
+4 +4
x+2y = 4
-x -x

2y = -x+4
divide both sides by 2

and I got -1/2x+2

I thought that the answer would be -2 maybe but its -8. How is it -8?

Answer 1

x + 2y - 4 = 0
x + 2y = 4
to find x-intercept, y = 0
x + 2(0) = 4
x = 4
x-intercept = (4.0)

slope intercept form (which you got right above) y = mx + b
for Line A is y = -1/2 x + 2
slope m = -1/2

If two lines are perpendicular, the slope of one is the negative reciprocal of the slope of the other.

Slope of Line B = ?
Line B through point (4,0)(line A and B have the same x-intercept)

To write equation of Line B
plug slope m in y = mx + b, and use point (4,0) to solve for b, which is the y-intercept.