Right equation of the line that is perpendicular to the line Y equals negative 3X +8 and passes through the point -2, 3. Right equation in point slope form

Question

asked May 14, 2023 86.4k views

1 Answer

Dracarys · Answer 1 · 2023-05-18T20:32:02+0000

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Perpendicular lines have slopes that are opposite reciprocals.

This means we take a number, flop it over, and change its sign.

In this case, we take
$\boxed{-3}$ , change its sign:

$\boxed{3}$

3 can also be written as

$\boxed{(3)/(1) }$

Now the numerator & denominator switch places:

$\boxed{(1)/(3)}$

So that's the slope of the new line.

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

$\bigstar{\underline{\boxed{\pmb{y-y_1=m(x-1)}}}$

Where

y₁ is the y-coordinate of the point (in this case, y₁ = 3)

m = slope (1/3)

x₁= the x-coordinate of the point (in this case, it's -2)

Plug in the values:-

$\bigstar{\boxed{\pmb{y-3=(1)/(3)(x-(-2)}}$

$\bigstar{\boxed{\pmb{y-3=(1)/(3)(x+2)} }\longleftarrow\sf{Point-Slope~Formula:)}}$

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