Lines Of Best Fit Worksheet Answers
1.
The graph above shows a line of best fit for data collected on the distance bicyclists have remaining in relation
to the amount of time they have been riding. What is the equation of the line of best fit?
A.
B.
C.
1. Pick two intersection points on the best fit line
(2 , 120 ) , ( 6 , 20 )
- green points on graph
2. Find the slope
D.
𝑚=
120 − 20
100
=
= −25
2−6
−4
3. Find “b” using one of your points
𝑦 = 𝑚𝑥 + 𝑏 and I used ( 6 , 20 )
20 = −25(6) + 𝑏
20 = −150 + 𝑏
170 = 𝑏
4. Plug 𝑚 and 𝑏 into 𝑦 = 𝑚𝑥 + 𝑏
𝑦 = −25𝑥 + 170
2.
The graph above shows a line of best fit for data collected on the amount earned by waiters and waitresses last
week in relation to the number of tables they served. What is the equation of the line of best fit?
A.
B.
1. Pick two intersection points on the best fit line
( 75 , 500 ) , ( 150 , 625 )
- green points on graph
2. Find the slope
C.
𝑚=
D.
625 − 500
125 5
=
=
150 − 75
75
3
3. Find “b” using one of your points
𝑦 = 𝑚𝑥 + 𝑏 and I used ( 75 , 500 )
5
500 = (75) + 𝑏
3
500 = 125 + 𝑏
375 = 𝑏
4. Plug 𝑚 and 𝑏 into 𝑦 = 𝑚𝑥 + 𝑏
𝑦=
5
𝑥 + 375
3
3. A small theme park is trying to determine the number of guests they should expect on a weekend, based on
the temperature outside.
Based on the trend line, about how many guests should be expected if the temperature is around 80°?
A. 8,300
B. 8
C. 7,300
D. 9,300
If we extend the best fit line, and then draw a vertical line through 80
degrees, we can see about 8,300 guests will be expected.
4. A group of students did an experiment to see how drinking cups of coffee right before bed affected sleep. The
results are shown below in the scatter plot with a line of best fit.
Use the given line of best fit to approximate the rate of change relative to the scatter plot above.
A.
Pick two intersection points on the best fit line
( 2 ,7 ) ,( 9 ,2 )
B.
Find the slope
C.
D.
𝑚=
7−2
5
= −
2−9
7
- blue points on graph
5.
The graph above shows a line of best fit for data collected on the amounts of cell phone bills in relation to the
number of minutes used. What is the equation of the line of best fit?
A.
Pick two intersection points on the best fit line
B.
( 200 , 20 ) , ( 400 , 25 )
C.
Find the slope
D.
𝑚=
- green points on graph
25 − 20
5
1
=
=
400 − 200
200 40
Find “b” using one of your points
𝑦 = 𝑚𝑥 + 𝑏 and I used ( 200 , 20 )
20 =
1
(200) + 𝑏
40
20 = 5 + 𝑏
15 = 𝑏
Plug 𝑚 and 𝑏 into 𝑦 = 𝑚𝑥 + 𝑏
𝑦=
1
𝑥 + 15
40
6.
Looking at the graph above showing a line of best fit, what is the correlation between the x and y variables?
A. y increases as x increases
B. y is constant
C. y decreases as x decreases
D. y decreases as x increases
7. A teacher made the following graph showing absences vs. final grades.
Predict the grade of a student that has 7 absences.
A. 50
B. 45
C. 70
D. 60
Sketch a line of best fit into the data.
Locate 7 absences and then read the corresponding
grade from the intersection…
8. Which scatterplot most likely has a line of best fit represented by y = -2x + 1?
W.
X.
Y.
Z.
A. X
We can rule out X and Z because they have a positive slope.
B. Z
C. Y
W has an approximate slope of − 2
D. W
Y has an approximate slope of −2
1
9.
The graph above shows a line of best fit for data collected on the amount of income earned by lawn companies
in relation to the number of yards mowed. What is the equation of the line of best fit?
A.
B.
Pick two intersection points on the best fit line
( 10 , 300 ) , ( 20 , 600 )
C.
Find the slope
D.
𝑚=
- green points on graph
600 − 300
300
=
= 30
20 − 10
10
Find “b” using one of your points
𝑦 = 𝑚𝑥 + 𝑏 and I used ( 10 , 300 )
300 = 30(10) + 𝑏
300 = 300 + 𝑏
0=𝑏
Plug 𝑚 and 𝑏 into 𝑦 = 𝑚𝑥 + 𝑏
𝑦 = 30𝑥
10.
The graph above shows a line of best fit for data collected on the value of used cars in relation to the number of
years since they were purchased. What is the equation of the line of best fit?
A.
Pick two intersection points on the best fit line
B.
( 4, 8000 ) , ( 8 , 5000 )
C.
Find the slope
D.
𝑚=
- green points on graph
8000 − 5000
3000
= −
= −750
4−8
4
Find “b” using one of your points
𝑦 = 𝑚𝑥 + 𝑏 and I used ( 4 , 8000 )
8000 = −750(4) + 𝑏
8000 = −3000 + 𝑏
11000 = 𝑏
Plug 𝑚 and 𝑏 into 𝑦 = 𝑚𝑥 + 𝑏
𝑦 = −750𝑥 + 11000
11. Mrs. Moises, the school counselor, keeps a candy jar in her office for students. During one week, she kept
count of how many students came to visit her and the number of candies in the jar, as shown in the scatter plot
below.
Based on the trend line, what is the best prediction for the number of candies in the jar when 30 students visit
her?
A. 90
If we extend the best fit line, and then draw a vertical line through 30
B. 180
students, we can see about 135 candies in the jar.
C. 135
D. 150
12.
Looking at the graph above showing a line of best fit, what is the correlation between the x and y variables?
A. y is constant
B. y increases as x increases
C. y increases as x decreases
D. y decreases as x increases
13. The graph below shows a line of best fit for data collected on the amount of time teenagers spend on the
computer and watching television.
Based on the line of best fit, how much time does a teenager spend watching television if they spend
120 minutes on the computer?
A. 150 minutes
B. 135 minutes
C. 165 minutes
D. 180 minutes
14. A teacher made the following graph showing the number of hours that a student studied for an exam versus
their exam grade.
Predict the grade of a student if they studied for 3.5 hours.
A. 80
B. 100
C. 95
D. 90
15.
The graph above shows a line of best fit for data collected on the price of a unit in relation to the number of
units sold. What is the equation of the line of best fit?
A.
Pick two intersection points on the best fit line
B.
( 200, 36 ) , ( 400 , 32 )
C.
Find the slope
D.
𝑚=
- green points on graph
36 − 32
4
1
= −
=−
200 − 400
200
50
Find “b” using one of your points
𝑦 = 𝑚𝑥 + 𝑏 and I used ( 200 , 36 )
36 = −
1
(200) + 𝑏
50
36 = −4 + 𝑏
40 = 𝑏
Plug 𝑚 and 𝑏 into 𝑦 = 𝑚𝑥 + 𝑏
𝑦=−
1
𝑥 + 40
50