Question

What is the equation for the points (-9,7) and (-6,-3)

Answer 1

In point slope form, the equation is y-7=(-10/3)(x+9).  In slope-intercept form, it is y=(-10/3)x-23.

First find the slope of the line.  The formula for slope is

m=(y₂-y₁)/(x₂-x₁)

Using our points, we have  

m=(-3-7)/(-6--9) = -10/3

Plug this into point slope form:

y-y₁=m(x-x₁)

y-7=(-10/3)(x--9)

y-7=(-10/3)(x+9)

Using the distributive property:

y-7=(-10/3)*x+(-10/3)*9

y-7=(-10/3)x-90/3

y-7=(-10/3)x-30

Add 7 to both sides:

y=(-10/3)x-23