The slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
Also, slope, m = (y2 - y1)/(x2 - x1)
x1 = 6, x2 = - 12
y1 = 8, y 2 = - 4
m = (- 4 - 8)/(- 12 - 6) = - 12/- 18 = 4/6
To determine the y intercept, we would substitute m = 4/6, x = 6 and y = 8 into the slope intercept equation. It becomes
8 = 4/6 * 6 + c
8 = 4 + c
c = 8 - 4 = 4
The equatiom would be
y = 4x/6 + 4