Exercise 27 Page 144

Practice makes perfect

a The given table shows the relationship between the cost of an international call and the length of the call.

Length of call (min)	1	2	3	4	5	6
Cost ($)	0.12	0.24	0.36	0.48	0.60	0.72

Let's plot these data points as ordered pairs on the coordinate plane.

The graph of the ordered pairs seem to be linear.

Extra

Linear and Nonlinear Functions

The general forms of the equations and a graph each function type are listed below.

b We can model the cost of an international call y as a function of the length of the call x by using a linear function. Let's recall the general form of a linear function.

y=mx+b Here, m is the slope and b is the y-intercept of the line. From the graph in Part A, we see that the y-intercept is 0. Let's substitute it into the function. y=mx+ b ⇔ y=mx+ 0 We can find m by substituting any ordered pair from the given table and simplifying. Let's use (1,0.12).

y=mx

SubstituteII

x= 1, y= 0.12

0.12=m( 1)

IdPropMult

Identity Property of Multiplication

0.12=m

RearrangeEqn

Rearrange equation

m=0.12

The slope of the linear function is 0.12. Then, the function below models the data. y= mx ⇓ y= 0.12x

c We can find the cost of a 10-minute call by substituting 10 for x in the model we found in Part B and simplifying. Let's do it!