Question

Find an equation for the line perpendicular to y = -1x + 8 with x-intercept at x = -4.

a) y = x + 3
b) y = -x - 3
c) y = x - 3
d) y = -x + 3

Answer 1

The equation for the line perpendicular to y = -1x + 8 with x-intercept at x = -4 is y = x + 4.

Step-by-step explanation:

To find the equation for the line perpendicular to y = -1x + 8 with an x-intercept at x = -4, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line has a slope of -1, so the slope of the line perpendicular to it would be 1. With the x-intercept at x = -4, we know that when x = -4, y = 0. Using the slope-intercept form y = mx + b, we have:

y = 1x + b

Plugging in the point (-4, 0) into the equation, we can solve for b:

0 = 1(-4) + b

0 = -4 + b

b = 4

Therefore, the equation for the line perpendicular to y = -1x + 8 with an x-intercept at x = -4 is y = x + 4 (option a) in the answer choices.