Question

Complete the equation of the line through (-9,7) & (-6,-3)

Answer 1

`y=-(10)/(3)x-23`

Explanation:

we have the points

(-9,7) and (-6,-3)

step 1

Find the slope

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

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

substitute the values

`m=(-3-7)/(-6+9)`

`m=-(10)/(3)`

step 2

Find the equation in point slope form

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

we have

`m=-(10)/(3)`

`(x1,y1)=(-6,-3)`

substitute

`y+3=-(10)/(3)(x+6)` ---> equation in point slope form

step 3

Find the equation of the line in slope intercept form

`y=mx+b`

we have

`y+3=-(10)/(3)(x+6)`

Isolate the variable y

Distribute right side

`y+3=-(10)/(3)x-20`

subtract 3 both sides

`y=-(10)/(3)x-20-3`

`y=-(10)/(3)x-23`