Question

Write an equation for a line perpendicular to Y=-4x-4 and passes through the points(12,5)

Answer 1

Hi!

I can help you with joy!

An equation for a line looks like so: y=mx+b

m = slope and b = y-intercept

Guide to Finding Equations of Lines:

Recall that perpendicular lines have slopes that

`\text{are opposite reciprocals}`.

Clarification: We take the slope, flop it over, and change its sign:

`\tt{y=-4x-4}\\Perpendicular:\\y=(1)/(4) (Slope)`

Equation:

(Point-Slope Form: y-y1=m(x-x1)

y-5=1/4(x-12)

y-5=1/4x-3

y=1/4x-3+5

y=1/4x+2 (Answer)

Hope it helps!

~Misty~

Answer 2

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

Explanation:

The equation of a line in slope- intercept form is

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

y = - 4x - 4 ← is in slope- intercept form

with slope m = - 4

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-4)` =
`(1)/(4)` , then

y =
`(1)/(4)` x + c ← is the partial equation

to find c substitute (12, 5 ) into the partial equation

5 = 3 + c ⇒ c = 5 - 3 = 2

y =
`(1)/(4)` x + 2 ← equation of perpendicular line