Fitting Lines

ID: nifub-munad
Created by Illustrative MathIllustrative Math
Subject: Algebra, Algebra 2
Grade: 8-9

Fitting Lines

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Problem 1

xy831028711591107931229712597127101120104127\begin{array}{|c|c|} \hline \\[-1em] x & y \\[-1em] \\ \hline \\[-1em] 83 & 102 \\[-1em] \\ \hline \\[-1em] 87 & 115 \\[-1em] \\ \hline \\[-1em] 91 & 107 \\[-1em] \\ \hline \\[-1em] 93 & 122 \\[-1em] \\ \hline \\[-1em] 97 & 125 \\[-1em] \\ \hline \\[-1em] 97 & 127 \\[-1em] \\ \hline \\[-1em] 101 & 120 \\[-1em] \\ \hline \\[-1em] 104 & 127 \\[-1em] \\ \hline \end{array}

1) Use graphing technology to create a scatter plot and find the best fit line. Round numbers to 2 decimal places.

2) What does the best fit line estimate for the yy value when xx is 100? Round numbers to 2 decimal places.

Problem 2

xy2.36.22.85.73.14.733.23.533.82.8\begin{array}{|c|c|} \hline \\[-1em] x & y \\[-1em] \\ \hline \\[-1em] 2.3 & 6.2 \\[-1em] \\ \hline \\[-1em] 2.8 & 5.7 \\[-1em] \\ \hline \\[-1em] 3.1 & 4.7 \\[-1em] \\ \hline \\[-1em] 3 & 3.2 \\[-1em] \\ \hline \\[-1em] 3.5 & 3 \\[-1em] \\ \hline \\[-1em] 3.8 & 2.8 \\[-1em] \\ \hline \end{array}

3) What is the equation of the line of best fit? Round numbers to 2 decimal places.

4) What does the equation estimate for yy when xx is 2.3? Round to 3 decimal places.

5) How does the estimated value compare to the actual value from the table when xx is 2.3?

6) How does the estimated value compare to the actual value from the table when xx is 3?

Problem 3

7) Which of these dot plots are best fit by the shown linear model?

A template for answering this question. Ask your instructor for an alternative.
a) Graph A\text{Graph A}b) Graph B\text{Graph B}c) Graph C\text{Graph C}d) Graph D\text{Graph D}
Problem 4

A seed is planted in a glass pot and its height is measured in centimeters every day.

The best fit line is given by the equation y=0.404x5.18y = 0.404x - 5.18, where yy represents the height of the plant above ground level, and xx represents the number of days since it first sprouted.

A template for answering this question. Ask your instructor for an alternative.

8) What is the slope of the best fit line?

9) What does the slope of the line mean in this situation?

10) Is it reasonable?

True or false? Write below.

11) What is the yy-intercept of the best fit line?

12) What does the yy-intercept of the line mean in this situation?

13) Is it reasonable?

True or false? Write below.
Problem 5

At a restaurant, the total bill and the percentage of the bill left as a tip is represented in the scatter plot.

The best fit line is represented by the equation y=0.632x+27.1y = -0.632x + 27.1, where xx represents the total bill in dollars, and yy represents the percentage of the bill left as a tip.

A template for answering this question. Ask your instructor for an alternative.

14) What does the best fit line estimate for the percentage of the bill left as a tip when the bill is $15?

Show Work

15) Is this reasonable?

True or false? Write below.

16) What does the best fit line predict for the percentage of the bill left as a tip when the bill is $50?

Show Work

17) Is this reasonable?

True or false? Write below.
Problem 6

18) A recent study investigated the amount of battery life remaining in alkaline batteries of different ages. The scatter-plot shows this relationship between the different alkaline batteries tested.

The scatter plot includes a point at (7, 15). Describe the meaning of this point in this situation.

A template for answering this question. Ask your instructor for an alternative.