Algebra Chapter 4 Functions And Linear Modeling Worksheet With Answers printable pdf download

Algebra Chapter 4 Functions And Linear Modeling Worksheet With Answers

Algebra

Answers

Name _______________________________________

CHAPTER 4

FUNCTIONS AND LINEAR MODELING

Period ______ Date ____________________________

Section 4.7: Lines of Best Fit Using Point-Slope Form

Example 1: The tread depth of a Michelin car tire was measured for different vehicles and different

distances driven. The table below shows x = the distance driven in thousands of miles and y = the tread

depth in millimeters.

a. Make a scatter plot of the

data on graph paper. Label

and scale your axis.

See attached graph

b. Use a ruler to draw the line

of best fit (trend line)

See attached graph

c. Pick two points that fall on

your line (probably not any

of the original given

points). Use these two

points to calculate the

slope m.

( ��, ��. �� ) �� (��, ��. ��)

��. �� − ��. ��

−��. ��

�� =

�� − ��

��

≈ −��. ��

d. Find units of measure for the slope, m, also known as rate of change. Using the context of the

problem, write a short sentence explaining the meaning of the slope in this problem.

−0.13��

meaning a loss of 0.13 mm of tread for every 1000 miles

1 ��ℎ��

( �� −

) to write the

e. Substitute the values of the slope and one point into the equation �� −

��

equation in point-slope form.

Using ( 4,6.8 )

�� − 6.8 = −0.13(�� − 4)

f. Write the equation of this line in slope-intercept form: �� = �� + ��. This equation gives us a

linear model for the tire tread depth based on the distance the vehicle was driven.

�� = −0.13�� + 7.32

g. What is the y-intercept of your model? Using the context of the problem, write a short sentence

explaining the meaning of the y-intercept in this problem.

7.32 meaning that when the tire is brand new, it will have 7.32 mm of tread

h. Use your linear model to predict the distance a car must be driven to have a remaining tire tread

depth of 1 millimeter.

1 = −0.13�� + 7.32 → �� = 48.6

�� 48,600 �� ℎ�� 1��.

Algebra Chapter 4 Functions And Linear Modeling Worksheet With Answers

Related Articles

Related forms

Related Categories