#### Solved Examples and Worksheet for Constructing Scatter Plots and Line of Fit

Q1The heights of different peaks are shown in the table. Identify the scatter plot that represents the data in the table.
 Peak Elevation (in ft) 1 6641 2 6660 3 6641 4 6680

A. Plot 4
B. Plot 1
C. Plot 2
D. Plot 3

Step: 1
Start at the origin on a scatter plot.
Step: 2
Move 1 unit to the right on the horizontal axis.
[To represent Peak 1.]
Step: 3
Move 6,641 units up from the horizontal axis and plot a point.
[The height of the peak 1 is 6,641 ft]
Step: 4
From the origin move 2 units to the right on the horizontal axis.
[To represent Peak 2.]
Step: 5
Move 6,660 units up from the horizontal axis and plot a point.
[The height of Peak 2 is 6,660 ft.]
Step: 6
From the origin move 3 units to the right on the horizontal axis.
[To represent Peak 3.]
Step: 7
Move 6,641 units up from the horizontal axis and plot a point.
[The height of Peak 3 is 6,641 ft.]
Step: 8
From the origin move 4 units to the right on the horizontal axis.
[To represent the Peak 4.]
Step: 9
Move 6,680 units up from the horizontal axis and plot a point.
[The height of Peak 4 is 6,680 ft.]
Step: 10
Plot 4 is the scatter plot that represents the data given in the table.
Correct Answer is :   Plot 4
Q2The number of boys and girls in different grades of a school are given in the table. Pick the appropriate scatter plot for the data.
 Grades Boys Girls 8th 80 25 9th 60 30 10th 40 35 11th 30 45 12th 20 65

A. Plot 3
B. Plot 1
C. Plot 2
D. Plot 4

Step: 1
The height of each point represent the number of students of a particular gender in a particular grade.
Step: 2
The yellow colored points in the scatter plots represent the number of boys and the blue colored points represent the number of girls in each grade.
Step: 3
Observe the scatter plots for the heights of the points to match with the values in the table.
Step: 4
It can be observed that the scatter plot given in Plot 3 exactly matches the values given in the table.
Step: 5
So, Plot 3 is the appropriate scatter plot graph for the data.
Correct Answer is :   Plot 3
Q3Choose the best fitting line for the data shown in the table and estimate the value of y when x is 9.
 x 0 2 4 6 8 10 y 42.29 39.83 37.37 34.91 32.45 29.99

A. y = - 1.23x + 43.29; 33.22
B. y = 1.23x + 42.29; 30.22
C. y = - 1.23x + 42.29; 31.22
D. y = - 123x + 42.29; 31.22

Step: 1
Plot the points of the data and draw the line that best fits the points.
Step: 2

Step: 3
Two points on the line are (0, 42.29) and (6, 34.91).
Step: 4
m = y2-y1x2-x1 =34.91-42.296-0 = - 1.23
[Slope of the line.]
Step: 5
y = mx + b
[Slope-intercept form.]
Step: 6
y = - 1.23x + 42.29
[Replace m with - 1.23 and b by 42.29.]
Step: 7
y = - 1.23(9) + 42.29 = 31.22
[Replace x with 9.]
Step: 8
At x = 9, the value of y is 31.22.
Correct Answer is :   y = - 1.23x + 42.29; 31.22
Q4Draw a scatter plot for the data and find the equation of the line that best fits the data.
 x - 1.2 0 0.6 1.5 2.4 3.3 3.6 y 3.2 2 1.4 0.5 - 0.4 - 1.1 - 1.6

A. Figure 2, y = - x + 2
B. Figure 1, y = x + 0.8
C. Figure 2, y = x - 2
D. Figure 1, y = - x + 1.6

Q5The scatter plot shows John's weight loss recorded on a weekly basis by his doctor. In the scatter plot y represents John's weight in pounds and x represents the time in weeks. Identify an equation for the line that best fits the data.

A. y = 52x + 170
B. y = - 52x + 170
C. y = - 2x + 170
D. y = 2x + 170

Q6Choose the best fitting line for the data shown in the table.
 x 0 2 4 6 8 y 6 6 15 20 24

A. x - 4y + 12 = 0
B. 9x + 4y + 24 = 0
C. 9x - y - 24 = 0
D. 9x - 4y + 24 = 0

Step: 1
Plot the points of the data and draw the line that best fits the points.
Step: 2

Step: 3
Two points on the line are (0, 6) and (8, 24).
Step: 4
m = y2-y1x2-x1 =24-68-0 = 94
[Slope of the line.]
Step: 5
y = mx + b
[Slope-intercept form.]
Step: 6
Line cuts y-axis at 6 so, y-intercept is 6.
Step: 7
y = 94x + 6
[Replace m with 94and b by 6.]
Step: 8
So, the best fitting line for the given data is 9x - 4y + 24 = 0
Correct Answer is :   9x - 4y + 24 = 0
Q7Draw a scatter plot for the data and find the equation of the line that best fits the data.
 x 0 1 2 3 4 5 6 y - 3 2 - 1 0 2 3 2

A. Figure 2, y = x + 3
B. Figure 1, y = x + 3
C. Figure 1, y = x - 3
D. Figure 2, y = x - 3

Step: 1
Plot the data as per the table.
Step: 2
Draw the line that best fit the points.
Step: 3

Step: 4
The two points that lie on the line are (3, 0) and (1, - 2).
Step: 5
m = y2-y1x2-x1
[Find slope of the best-fitting line.]
Step: 6
m = - 2 - 01 - 3 = 1
[Substitute and simplify.]
Step: 7
Find the y-intercept of the line using slope-intercept form.
Step: 8
y = mx + b
[Write slope-intercept form.]
Step: 9
0 = 1(3) + b
[Replace m with 1, x with 3, and y with 0.]
Step: 10
b = - 3
Step: 11
So, the equation of the best-fitting line is y = x - 3.
[Use y = mx + b.]

Correct Answer is :   Figure 2, y = x - 3
Q8Choose an equation that best fits the data for the scatter plot shown.

A. y = 32x + 92
B. y = 34x + 92
C. y = 34x - 92
D. y = 3x + 92

Step: 1
Draw the line that best fit the points.
Step: 2

Step: 3
Two points that lie on the line are (- 2, 3) and (2, 6).
Step: 4
m = y2-y1x2-x1
[Find slope of the best-fitting line.]
Step: 5
m = 6-32-(-2) = 34
[Substitute and simplify.]
Step: 6
Find the y-intercept of the line using slope-intercept form.
Step: 7
y = mx + b
[Write slope-intercept form.]
Step: 8
3 = 34(- 2) + b
[Replace m with 34, x with - 2, and y with 3.]
Step: 9
3 + 32 = b
[Simplify.]
Step: 10
b = 92
Step: 11
An equation of the best-fitting line is y = 34x + 92.
Correct Answer is :   y = 34x + 92
Q9Choose an equation that best fits the data for the scatter plot shown.

A. 2x - 5y - 14 = 0
B. 5x - 2y + 14 = 0
C. 2x - 5y + 14 = 0
D. 2x + 5y + 14 = 0

Step: 1
Draw the line that best fit the points.
Step: 2

Step: 3
Two points that lie on the line are (3, 4) and (- 2, 2).
Step: 4
m = y2-y1x2-x1
[Find slope of the best-fitting line.]
Step: 5
m = 2-4-2-3 = 25
[Substitute and simplify.]
Step: 6
Find the y-intercept of the line using slope-intercept form.
Step: 7
y = mx + b
[Write slope-intercept form.]
Step: 8
4 = 25(3) + b
[Replace m with 25, x with 3, and y with 4.]
Step: 9
4 - 65 = b
[Simplify.]
Step: 10
b = 145
Step: 11
y = 25x + 145
Step: 12
An equation of the best-fitting line is 2x - 5y + 14 = 0.
Correct Answer is :   2x - 5y + 14 = 0
Q10Choose an equation that best fits the data for the scatter plot shown.

A. 11x - 6y - 26 = 0
B. 11x + 6y - 26 = 0
C. 11x + 6y + 26 = 0
D. 11x - 6y + 26 = 0

Step: 1
Draw the line that best fit the points.
Step: 2

Step: 3
Two points that lie on the line are (- 4, - 3) and (2, 8).
Step: 4
m = y2-y1x2-x1
[Find slope of the best-fitting line.]
Step: 5
m = 8-(-3)2-(- 4) = 116
[Substitute and simplify.]
Step: 6
Find the y-intercept of the line using slope-intercept form.
Step: 7
y = mx + b
[Write slope-intercept form.]
Step: 8
- 3 = 116(- 4) + b
[Replace m with 116, x with - 4, and y with - 3.]
Step: 9
- 3 + 223 = b
[Simplify.]
Step: 10
b = 133
Step: 11
y = 116x + 133
Step: 12
An equation of the best-fitting line is 11x - 6y + 26 = 0.
Correct Answer is :   11x - 6y + 26 = 0
Q11The following table shows the Percentage of Males who smoke and their Life Expectancy in different countries. Select the appropriate scatter plot for the data.
 Countries Percentage of male who smoke Male Life Expectancy USA 28 72.4 Denmark 35 71.3 France 39 73.3 Germany 35.4 72.2 Italy 37 73.5 Norway 35.7 73.8 Poland 50 67.6 Brazil 38.4 56.4 India 38 57.2 China 60 65.8 Iraq 38 63.5 Japan 58 75.2 Kuwait 51 71.6

A. Graph 3
B. Graph 4
C. Graph 1
D. Graph 2

Step: 1
On a graph paper, represent the "Percentage of males who smoke" along x - axis and "Male Life Expectancy" along y - axis.
Step: 2
Plot the values on the graph, corresponding with those given in the table. The scatter plot should look like the one below.
Step: 3
So, Graph 2 is the appropriate scatter plot for the data.
Correct Answer is :   Graph 2
Q12The following table shows the weights (in g) of ten books and the number of pages in each book. Pick an appropriate scatter plot for the data.
 Number of pages Weight (in g) 90 178 100 198 80 158 155 330 125 250 145 310 140 280 160 320 135 250 100 178

A. Graph 4
B. Graph 2
C. Graph 1
D. Graph 3

Step: 1
On a graph paper, represent the "Number of pages" along x - axis and "Weight (in g)" along y - axis.
Step: 2
Plot the values on the graph, corresponding with those given in the table. The scatter plot should look like the one below.
Step: 3
So, Graph 2 is the appropriate scatter plot for the data.
Correct Answer is :   Graph 2
Q13The following table shows the ages (in years) and annual incomes (thousands of dollars) of 10 members. Pick an appropriate scatter plot for the data.
 Age (in years) Annual Income (thousands of dollars) 26 36 29 76 33 35 33 38 34 37 46 45 48 61 54 52 55 59 59 69

A. Graph 2
B. Graph 1
C. Graph 3
D. Graph 4

Step: 1
On a graph paper, represent the "Age (in years)" along x - axis and "Annual Income (thousands of dollars)" along y - axis.
Step: 2
Plot the values on the graph, corresponding with those given in the table. The scatter plot should look like the one below.
Step: 3
So, Graph 3 is the appropriate scatter plot for the data.
Correct Answer is :   Graph 3
Q14The following table shows the height (in cm) and Intelligent Quotient of eight students in a class. Select the appropriate scatter plot for the data.
 Height (in cm) Intelligent Quotient 131 90 146 90 101 120 179 102 156 115 121 98 148 103 167 105

A. Graph 1
B. Graph 3
C. Graph 2
D. Graph 4

Step: 1
On a graph paper, represent the "Height (in cm)" along x - axis and "Intelligent Quotient" along y - axis.
Step: 2
Plot the values on the graph, corresponding with those given in the table. The scatter plot should look like the one below.
Step: 3
So, Graph 4 is the appropriate scatter plot for the data.
Correct Answer is :   Graph 4
Q15The following table shows the weights (in kg) and waist sizes of ten persons. Select the appropriate scatter plot for the data.
 Weight (in kg) Waist size (in cm) 86 100 64 70 51 61 93 112 86 87 78 86 58 70 63 82 44 57 76 84

A. Graph 2
B. Graph 4
C. Graph 3
D. Graph 1

Step: 1
On a graph paper, represent the "Weight (in kg) along x - axis and "Waist size (in cm)" along y - axis.
Step: 2
Plot the values on the graph, corresponding with those given in the table. The scatter plot should look like the one below.
Step: 3
So, Graph 3 is the appropriate scatter plot for the data.
Correct Answer is :   Graph 3
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