The equation in red:
Slope = 5-(-3)/-1-1
Slope = 8/-2 = -4
The eq of the function is
y = -4x + 1
The equation in black:
Slope=4/4 = 1
The equation of the function is
y = x - 4
Solving the two equations:
Subtract 1 from 2
-4x +1 - x + 4 = 0
-5x = -5 so x = 1
Replacing in the second equation
y = 1 - 4 = -3
