Title: Lesson 8-8
Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 7-8

Age
(months)

Height
(in.)

2 | 19
8 | 23
1 | 21.5
12 | 22.5
5 | 20
6 | 22.25
Example 1	Make Predictions from a Line of Fit
CHILDREN	The table shows the age (in months) and the height (in inches) of infants.

a.  Make a scatter plot and draw a line of fit for the data.

b.  Use the line of fit to predict the height of a 16 month old child.
Extend the line so that you can find the y value for an x value of 16.  The y value for 16 is about 25.  So, a prediction for the height of a 16 month old child is approximately 25 inches.

Real-World EXAMPLE 
Example 2	Make Predictions from an Equation
HEATING BILL	The scatter plot shows the relationship between average monthly temperature during the winter and the corresponding heating bill for that month.

a.  Write an equation in slope-intercept form for the line of fit that is drawn.
Step 1
First, select two points on the line and find the slope.  We have chosen (40, 100) and (20, 175).  Notice that they are not original data points.
  m = 		Definition of slope
	= 		(x_1, y_1) = (40, 100); (x_2, y_2) = (20, 175)
	= -3.75			Simplify.

Step 2
Next, find the y-intercept.
    y = mx + b		Slope-intercept form
100 = -3.75(40) + b	Replace (x, y) with (40, 100) and m with –3.75.
250 = b			Simplify.

Step 3
Write the equation.
y = mx + b			Slope-intercept form
y = -3.75x + 250		Replace m with –3.75 and b with 250.

b. 	Predict the monthly heating bill for a winter month having average temperature of 10°F.
y = -3.75x + 250		Write the equation of the line of fit.
y = -3.75(10) + 250	Replace x with 10.
y = 212.5			Simplify.

A prediction for the monthly heating bill for a winter month in which the average temperature is 10° F is $212.50.