Exercise 8 Page 199

Start with writing the ordered pairs from the table. Use them to calculate the slope and y-intercept.

Slope: 59, monthly cost of the membership.
Y-intercept: 100, initial membership fee.
Equation: C=59m+100
Cost of 4-month membership: $336

Practice makes perfect

From the table, we can list the following ordered pairs. (0,100), (3,277), (6,454)

Find the slope and y-intercept

We can use these points to calculate the slope and y-intercept. First, let's substitute two of them into the Slope Formula and simplify.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,100) & ( 3,277)

m=277- 100/3- 0

▼

Simlplify

SubTerms

Subtract terms

m=177/3

CalcQuot

Calculate quotient

m=59

The slope is 59. To calculate the y-intercept b, we can substitute the slope and one of the points in slope-intercept form of the equation.

y=mx+b

SubstituteII

x= 0, y= 100

100=m* 0+b

Substitute

m= 59

100=59*0+b

ZeroPropMult

Zero Property of Multiplication

100=b

RearrangeEqn

Rearrange equation

b=100

Thus, the y-intercept is 100. Let's now think of what these values mean.

Interpretation

The slope is multiplied by x, which represents the number of months. Therefore, we can conclude that $59 is the monthly cost. The y-intercept b is the constant in slope-intercept form. It's added only one time. This is the same as the initial membership fee, it should be paid only once in the beginning.

Writing the equation

Let's now write the equation in slope-intercept form. For the meaning of the equation to be more clear, we can write C (cost) instead of y and m (months) instead of x. C=59m+100