Complete the equations of the line through (-9,7) and (-6,-3)

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