Question

Find the equation of the line that is perpendicular to the line Y equals negative 4X -4 and passes through the point -2, -4. Write the equation in point slope form

Answer 1

hello!

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Perpendicular lines have slopes that are opposite reciprocals.

This means we take the slope, flop it over, and change its sign.

In this case, we have

`\boxed{-4}`

First, flop it over:

`\boxed{-(1)/(4)}`

Change its sign:

`\boxed{(1)/(4)}`

Now, let's write the equation of the line in point-slope form:-

`\bigstar\boxed{\pmb{y-y1=m(x-x1)}}\longleftarrow\sf{Point-Slope~Formula}`

Where

y₁ is the y-coordinate of the point that the line intersects

m is the slope of the line

x₁ is the x-coordinate of the point that the line intersects

In this case,

y₁ is equal to -4

m is equal to
`\boxed{(1)/(4) }`

x₁ is equal to -2

Plug in the values:-

`\bigstar{\boxed{y-(-4)=(1)/(4)(x-(-2)}`

Simplify:-

`\longrightarrow\sf{y+4=(1)/(4) (x+2)`

and we're done!

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note:-

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)