need help with algebra

Question

write an equation of the line passing through the point,(4,-1) and perpendicular to the line y=2x-5

Answer 1

Hello Ivonne,

When 2 lines are perpendicular, the product of their slopes equals -1. Applying this rule to this problem:

(2) * (slope_of_perpendicular_line) = -1 ---> slope_of_perpendicular_line = -1/2

The slope-intercept equation of the line you're looking for is y = (-1/2)*x + b

To find b: replace x and y by 4 and -1 because that line passes through the point (4,-1)

You get: -1 = (-1/2)*4 + b --> -1 = -2 + b ---> b = 1

So the equation of the line passing through (4,-1) and perpendicular to y = 2x - 5 is:

y = (-1/2)*x + 1