Passing through (4,-5) and perpendicular to the line who’s equation is y=1/2x+1

Question

Write equation in point-slope form and slope-intercept form

Answer 1

Perpendicular lines have inverse slopes of opposites signs

Line

y = 1/2x + 1

m = 1/2

A line perpendicular to this has a slope m that is the negative inverse or (-1/m)

m = -(2/1) or -2

slope is -2

Since the line passes through (4, -5) this can be used to calculate b in the slope intercept form

y = mx + b

-5 = -2(4) + b

-5 = -8 + b

Add 8 to both sides

-5 + 8 = b

3 = b

So the perpendicular line is

y = -2x + 3

Point slope form is

-2(x - 4) = (y -(-5))

-2(x -4) = (y + 5)

Answer 2

The slope of y = 1/2x + 1 is 1/2. The slope of the line perpendicular to that is -2 (perpendicular lines have a slope equal to the negative reciprocal). So the slope of the line we are looking for is -2. It goes through (4, -5). You can use the point-slope form [y - y₁ = m(x - x₁)] so the equation is y + 5 = -2(x - 4).