Question

What is the y-intercept of a line perpendicular to y= 1/2x + 6 that passes through the point (4,-3)

Answer 1

(0,5)

Explanation:

Perpendicular lines have slopes which are negative reciprocals of each other. The slope of the line y=1/2x + 6 is 1/2. The slope perpendicular to it is -2.

Using m=-2, substitute it and (4,-3) into the point slope form and simplify to find the y-intercept.

`y-y_1 = m(x-x_1)\\y--3=-2(x-4)\\y+3=-2(x-4)\\y+3=-2x+8\\y=-2x+5`

The equation is now in slope intercept form y=mx+b and b is the y-intercept. The y-intercept of y=-2x+5 is (0,5).