What is the equation of the line that passes through the point (-1, 5) and has a slope of −3?

Question

asked Aug 1, 2024 173k views

1 Answer

Lenglei · Answer 1 · 2024-08-06T05:15:00+0000

The answer is:

In point slope:

$\rm{y-5=-3(x+1)}$

In slope intercept:

$\rm{y=-3x+2}$

Work/explanation:

Given:

To find the equation of the line, I'm going to use point slope:

$\sf{y-y_1=m(x-x_1)}$

Where the slope is m and the point is (x₁, y₁).

So our point-slope is:

$\rm{y-5=-3(x-(-1)}$

Let's simplify.

$\rm{y-5=-3(x+1)}$

That's our equation in point slope.

__________________________

We might want to write the equation in slope intercept (y = mx + b).

We can do that, too, but let's simplify first.

We take our point slope equation.

We simplify the right side.

$\rm{y-5=-3x-3}$

Add 5 on both sides

$\rm{y=-3x+2}$