Question

Which of the following is the equation of a line perpendicular to

4y = 2x + 5 that passes through (-1, -1)?
A.
y - 2x = -3
B.
2y - 2x = 10
C.
y = -2x - 3
D.
y = -2x - 6

Answer 1

Answer:
`y = -2x - 3`

Explanation:

Two lines are said to be perpendicular if the product of their slope = -1

Given :

`4y = 2x + 5`

to find the slope , we will write it in the form :
`y = mx + x`

That is

`y = (2)/(4)x + (5)/(4)`

`y = (1)/(2)x + (5)/(4)`

which means that the slope =
`(1)/(2)`

any line that is perpendicular to this line will have slope = -2

using the formula :

`y - y_(1) = m (x-x_(1))` , we have

`y - (-1) = -2 ( x -(-1) )`

`y + 1 = - 2 ( x + 1 )`

`y + 1 = -2x - 2`

`y = -2x - 2 - 1`

`y = -2x - 3`