Exercise 58 Page 196

Points that lie on the same line are called collinear points. If the given points are collinear, the slope between every pair of points will be equal. To determine the slope between each pair of points, we will use the Slope Formula. m = y_2-y_1/x_2-x_1We will calculate the slope between A and B, B and C, and A and C. Let's start with A and B. Note, when we substitute the points into the Slope Formula, it does not matter which we use for (x_1,y_1) or (x_2,y_2).

m_(AB)=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 5,6) & ( 3,2)

m_(AB)=2- 6/3- 5

SubTerms

Subtract terms

m_(AB)=-4/-2

DivNegNeg

- a/- b=a/b

m_(AB)=4/2

CalcQuot

Calculate quotient

m_(AB)=2

We can calculate the other two slopes in the same way.

Points	y_2-y_1/x_2-x_1	m
A( 5,6), B( 3,2)	2- 6/3- 5	2
B( 3,2), C( 6,8)	8- 2/6- 3	2
A( 5,6), C( 6,8)	8- 6/6- 5	2

Notice that all pairs of points have a slope of 2. Thus, all points in the given set lie on the same line.