AnswersPre-Algebra BConstructing Scatterplots

Using Equations to Represent Trend Lines Answers

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Melanie and Tracy are each finding the equation of the trend line that fits the data in the table below. Participation in the School BandYearNumber of students201048201152201255201359Melanie uses the ordered pairs (2010, 48) and (2013, 59) to find her equation. Tracy defines x as the number of years since 2010 and uses the ordered pairs (0, 48) and (3, 59) to find her equation. How will the two girls’ equations compare?

A
They will have the same slopes and the same y-intercepts.
B
They will have the same slopes but different y-intercepts.
C
They will have different slopes but the same y-intercepts.
D
They will have different slopes and different y-intercepts.
2
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What is the slope of the line of best-fit in the scatterplot below?

Question illustration
A
StartFraction 9 Over 27 EndFraction
Option A
B
StartFraction 3 Over 7 EndFraction
Option B
C
StartFraction 7 Over 3 EndFraction
Option C
D
StartFraction 27 Over 9 EndFraction
Option D
3

Jeremy surveyed students in his class about their spending habits in the school cafeteria. He used the data to create a scatterplot.How Students Spend Money in the Cafeteria Which is the equation of his trend line?

Question illustration
A
y = 2.75 x
Option A
B
y = 3.05 x minus 0.6
Option B
C
y = 3.25 x minus 1
Option C
D
y = 9.75 x minus 14
Option D
4

Miguel is calculating the slope of a line of best-fit in the scatterplot below. Which pair of points would be best for Miguel to use?

Question illustration
A
P and W
B
Q and V
C
R and U
D
S and T
5

Mia’s work to find the slope of a trend line through the points (3, 10) and (35, 91) is shown below.Mia’s WorkStep 1Step 2Step 3What was the first error that Mia made?

Question illustration
A
Mia simplified incorrectly and made the slope positive.
B
Mia subtracted in the wrong order.
C
Mia switched the numerator and the denominator.
D
Mia used subtraction instead of addition.
6

Which pair of points should be used to find the line of best-fit for the scatterplot?.

Question illustration
A
J and L
B
J and M
C
K and L
D
K and M
7

Andrea’s work to find the equation of a trend line through the points (48, 61) and (72, 195) is shown below.Andrea’s Work Step 1Step 2Step 3Step 4What was the first error that Andrea made?

Question illustration
A
Andrea used the reciprocal of the slope.
B
Andrea made a computational error when she simplified m.
C
Andrea substituted incorrectly when she solved for b.
D
Andrea made a sign error when she solved for b.
8

Which is the equation of a trend line that passes through the points (7, 450) and (14, 401)?

A
y = negative 7 x + 499
Option A
B
y = negative StartFraction 1 Over 7 EndFraction x + 451
Option B
C
y = StartFraction 1 Over 7 EndFraction x + 449
Option C
D
y = 7 x + 401
Option D
9

Which expression can be simplified to find the slope of the trend line in the scatterplot?

Question illustration
A
StartFraction 21 minus 35 Over 8 minus 4 EndFraction
Option A
B
StartFraction 8 minus 4 Over 21 minus 35 EndFraction
Option B
C
StartFraction 35 minus 21 Over 8 minus 4 EndFraction
Option C
D
StartFraction 8 minus 4 Over 35 minus 21 EndFraction
Option D
10

Jordan is calculating the slope of the trend line in the scatterplot below. How can Jordan use the plot to check the reasonableness of his answer?

Question illustration
A
His slope should be positive because the coordinates of all the plotted points are positive.
B
His slope should be positive because the trend line is slanted up to the right.
C
His slope should be negative because there are plotted points not on the line.
D
His slope should be negative because the x-coordinate of each plotted point is less than the y-coordinate.

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