Find the value of c such that the three points (5,5), (3,1), and (-6,c) lie on the same line. Note: Three points are on the same line if the slope of the line through any two points is always the same.
Find the slope of (5,5) and (3,1). That is equal to rise/run = -4/-2 = 2.
y = 2x + c
Plugin the information given: 5 = 2(5) + c
Solve: 5 = 10 + c -> c = -5
Equation: y=2x-5
Plugin the information: y = 2(-6) - 5
Solve: y = -12 - 5 -> y = -17
C = 17