Question

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5 ? Enter your answer in the box.

Answer 1

`y = (3)/(2) x-11`

Explanation:

We have to find the equation a line which passes through the point (8, 1) and is perpendicular to a line with the equation
`y = - (2)/(3) x+5`.

So the slope for this equation will be the negative reciprocal of the line which is perpendicular to it i.e.
`(3)/(2)`.

Finding the y-intercept of the line:

`y=mx+c`

`1=(3)/(2) (8)+c`

`c=-11`

Therefore, the equation of the line will be
`y = (3)/(2) x-11`.

Answer 2

y =
`(3)/(2)` x - 11

Explanation:

the equation of a line in slope- intercept form is

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

y = -
`(2)/(3)` x + 5 is in this form

with m = -
`(2)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(2)/(3) )` =
`(3)/(2)`, hence

y =
`(3)/(2)` x + c ← is the partial equation

to find c substitute (8, 1) into the partial equation

1 = 12 + c ⇒ c = 1 - 12 = - 11

y =
`(3)/(2)` x - 11 ← equation of line