Question

Write the equation of the line that passes through the points (2,-6) and (-2,-4).

Answer 1

Slope = (-4-(-6) /  (-2-2)  = 2/-4 = -1/2   You are correct.

Now plug in the point ( 2 , -6)  into the formally you mentioned above:-

y - (-6) = (-1/2)(x - 2)

y + 6  = (-1/2)(x - 2)

to get rid of the fraction you can multiply through by  2:-

2y + 12 = -1(x - 2)

2y + 12 = -x + 2

in standard form the equation is 

x + 2y = -10