Question

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

Answer 1

The answer is:

In point slope:

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

In slope intercept:

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

Work/explanation:

Given:

• point : (-1, 5)
• slope : -3

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}`

This is our equation in slope intercept.