Question

A line passes through (1, –5) and (–3, 7).Write an equation for the line in point-slope form.

Rewrite the equation in slope-intercept form.

Answer 1

part 1) The equation of the line in point slope form is
`y+5=-3(x-1)`

Part 2) The equation in slope intercept form is
`y=-3x-2`

Step-by-step explanation:

Part 1) Write an equation for the line in point-slope form

we have the points

(1, –5) and (–3, 7)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(7+5)/(-3-1)`

`m=(12)/(-4)`

`m=-3`

Find the equation of the line into point slope form

`y-y1=m(x-x1)`

we have

`m=-3`

`point\ (1,-5)`

substitute

`y+5=-3(x-1)` ----> equation of the line in point slope form

Part 2) Rewrite the equation in slope-intercept form.

`y=mx+b`

we have

`y+5=-3(x-1)`

Convert to slope intercept form

Isolate the variable y

Distribute right side

`y+5=-3x+3`

Subtract 5 both sides

`y=-3x+3-5`

`y=-3x-2`