# Fitting Lines

Illustrative Math
Subject: Algebra, Algebra 2

# Fitting Lines

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##### Problem 1

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

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 ﻿$y$﻿ value when ﻿$x$﻿ is 100? Round numbers to 2 decimal places.

##### Problem 2

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

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

4) What does the equation estimate for ﻿$y$﻿ when ﻿$x$﻿ is 2.3? Round to 3 decimal places.

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

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

##### Problem 3

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

a) $\text{Graph A}$b) $\text{Graph B}$c) $\text{Graph C}$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 ﻿$y = 0.404x - 5.18$﻿, where ﻿$y$﻿ represents the height of the plant above ground level, and ﻿$x$﻿ represents the number of days since it first sprouted.

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 ﻿$y$﻿-intercept of the best fit line?

12) What does the ﻿$y$﻿-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 ﻿$y = -0.632x + 27.1$﻿, where ﻿$x$﻿ represents the total bill in dollars, and ﻿$y$﻿ represents the percentage of the bill left as a tip.

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.