Question

• Which of the following equations represents a line that is perpendicular to

y = --4x+9 and passes through the point, (4, 5)?
A. y = -4x+4
B. y = 1/4x+5
C. y = 1/4x+4
D. y = 1/4x+6

Answer 1

C

Explanation:

The equation of a line in slope- intercept form is

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

y = - 4x + 9 ← is in slope- intercept form

with slope m = - 4

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

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

y =
`(1)/(4)` x + c ← is the partial equation of the perpendicular line

To find c substitute (4, 5) into the partial equation

5 = 1 + c ⇒ c = 5 - 1 = 4

y =
`(1)/(4)` x + 4 ← equation of perpendicular line → C