Algebra Chapter 4 Functions And Linear Modeling Worksheet With Answers (Page 2 of 5) in pdf

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

Example 2: Scuba divers in Hawaii reported the pressure experienced at different depths underwater.

The table below shows x = the depth measured in feet and y = pressure measured in pounds per square

inch (psi.)

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. Use these two points to calculate the

slope m.

( ��, �� ) �� (��, ��)

�� − ��

��

�� =

≈ ��. ��

�� − ��

��

d. Find units of measure for the slope, m. Using the context of the problem, write a

short sentence explaining the meaning of the slope in this problem.

30��

0.53��

meaning the pressure increases by 0.53 psi every foot you descend.

57��

1��

e. Write the equation of the line of best fit in point-slope form.

Using ( 12,20 )

�� − 20 = 0.53(�� − 12)

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

linear model for the underwater pressure based on the depth of the diver.

�� = 0.53�� + 13.64

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.

13.64 meaning that when the diver is at the surface, the pressure is 13.64 psi

Use your linear model to predict the depth of a diver experiencing a pressure of 75 psi.

�� = 0.53 ( 75 ) + 13.64 = 53.39

�� 53 ��

Example 3: Several students at an elementary school measured the length of their right foot and their

height. The table below shows x = the foot length in centimeters and y = the height also in centimeters.

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. Use these two points to calculate the

slope m.

( ��, �� ) �� (��, ��)

�� − ��

��

�� =

= ��. ��

�� − ��

��

d. Find units of measure for the slope, m. Using the context of the problem, write a

short sentence explaining the meaning of the slope in this problem.

11��

2��

= 5.5 �� ℎ�� 11 �� 2 �� 5.5 �� 1 �� ℎ��ℎ�� ℎ

e. Write the equation of the line of best fit in point-slope form.

�� ( 22,148 )

�� − 148 = 5.5 ( �� − 22 )

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

linear model for the height of a student based on the length of his/her right foot.

�� = 5.5�� + 27

Algebra Chapter 4 Functions And Linear Modeling Worksheet With Answers Page 2

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