What is the equation of the line that is perpendicular to and has the same y-intercept as the given line?

a. y = x + 1
b. y = x + 5
c. y = 5x + 1d.
y = 5x + 5

ANSWER

The required equation is



EXPLANATION

The given line passes through the point



The slope of this line is given by the formula,



This implies that,





The product of the slope of the two perpendicular lines should be negative one.

Thus,


This implies that,



We multiply through by

to obtain,




Therefore the slope of the line perpendicular to the given line is


We use the slope intercept formula


where

is the y-value of the y-intercept.

We therefore have,



as the required equation.

The correct answer is C.