Question

Which equation represents the line that is perpendicular to y = 3/4x+ 1 and passes through (-5,11)A.y=-4/3x+13/3B.y=-4/3x+29/3C.y=3/4x+59/4D.y=3/4x-53/4

Answer 1

A.y=-4/3x+13/3

Explanation:

The equation of a line has the following format:

y = ax + b

In which a is the slope.

Perpendicular to y = 3/4x+ 1:

Two lines are perpendicular if the multiplication of their slopes is -1.

Here the slope is 3/4.

In the answer to this exercise, the slope is a.

So

`(3)/(4)\ast a=-1`
`(3a)/(4)=-1`

Now, cross multiplication

3a = -4

a = -4/3

So, for now, the equation is:

y = (-4/3)x + b

Passes through (-5,11):

This means that when x = -5, y = 11. So

11 = (-4/3)*(-5) + b

11 = (20/3) + b

b = 11 - (20/3)

`11-(20)/(3)=((3)/(1)\ast11-(3)/(3)\ast20)/(3)=(33-20)/(3)=(13)/(3)`

So the correct answer is:

A.y=-4/3x+13/3