Question

the slope-intercept form of the equation of a line that passes through point (–2, –13) is y = 5x – 3. What is the point-slope form of the equation for this line?

Answer 1

y+13 = 5(x+2) is point-slope form of the equation for this line.

Explanation:

We have given a point and slope-intercept of the equation of line.

Let (x₁,y₁) = (-2,-13) and y = 5x-3

y-y₁ = m(x-x₁) is point-slope form of equation of line where m denotes slope of the line.

We have to find point-slope form of the equation of line.

Since, we know that y = mx+c is slope-intercept form of the line where m denotes slope of line.

From slope-intercept form, m = 5

Putting values in point-slope form ,we have

y-(-13) = 5(x-(-2))

y+13 = 5(x+2) is point-slope form of the equation for this line.

Answer 2

Answer:
`(y+13)=5(x+2)`

Explanation:

The equation of the line in slope-intercept form is:

`y=mx+b`

Where m is the slope and b is the y-intercept.

The point-slope form of the equation of the line is:

`(y-y_1)=m(x-x_1)`

Where m is the slope of the line and (
`x_1,y_1`) is a point of the line.

You know that line that passes through point (-2, -13) and the slope is 5, then you must substitute them into the equation.

Therefore, you obtain:

`(y-(-13))=m(x-(-2))`

`(y+13)=5(x+2)`