Answer:
[tex]y=-\frac{10}{3}x-23[/tex]
Step-by-step 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
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-3-7}{-6+9}[/tex]
[tex]m=-\frac{10}{3}[/tex]
step 2
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{10}{3}[/tex]
[tex](x1,y1)=(-6,-3)[/tex]
substitute
[tex]y+3=-\frac{10}{3}(x+6)[/tex] ---> equation in point slope form
step 3
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]y+3=-\frac{10}{3}(x+6)[/tex]
Isolate the variable y
Distribute right side
[tex]y+3=-\frac{10}{3}x-20[/tex]
subtract 3 both sides
[tex]y=-\frac{10}{3}x-20-3[/tex]
[tex]y=-\frac{10}{3}x-23[/tex]
