Question

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 1

C. 5x+1

Explanation:

edge2020

Answer 2

ANSWER

The required equation is


`y = 5x + 1`



EXPLANATION

The given line passes through the point


`(5,0) \: and \: (0,1)`


The slope of this line is given by the formula,


`m=(y_2-y_1)/(x_2-x_1)`


This implies that,


`m = (1 - 0)/(0 - 5)`


`m = - (1)/(5)`


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

Thus,


`m_1* m_2=-1`
This implies that,



`- (1)/(5) * m_2=-1`


We multiply through by

`- 5`
to obtain,



`m_2=-1 * - 5`


`m_2=5`
Therefore the slope of the line perpendicular to the given line is

`5.`


We use the slope intercept formula

`y =m x + b`

where

`b = 1`
is the y-value of the y-intercept.



We therefore have,



`y = 5x + 1`

as the required equation.


The correct answer is C.