Question

What is the equation of the line perpendicular to y=1/4x-5 through the point (4,-3)

Answer 1

y = - 4x + 13

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the equation

y =
`(1)/(4)` x - 5 ← in slope- intercept form

with slope m =
`(1)/(4)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(4) )` = - 4 , then

y = - 4x + c ← is the partial equation

to find c , substitute (4, - 3 )for x and y in the partial equation

- 3 = - 4(4) + c = - 16 + c ( add 16 to both sides )

13 = c

y = - 4x + 13 ← equation of perpendicular line