Basics
(0, b) = yintercept = slopeintercept = point where line crosses yaxis
A question involving slopeintercept will often require you to use two points to calculate the slope and yintercept on the way to writing the equation of a line.
Although plotting points and a line on an xy coordinate plane or grid can help visualize the process, a question involving slopeintercept can often be solved without graphing.
Formulas (Mathematics Formula Sheet)
slopeintercept form of the equation of a line
y = mx + b
slope of a line
m =
Formulas (NOT on Mathematics Formula Sheet)
slopeintercept b
b = y – mx
Question
Using the points (1, 4) and (3, 9) in the graph below, write the slopeintercept equation for Line L. The slope and yintercept should be in decimal form.
Answer
y = 2.5x + 1.5
Answer Process
(x_{1}, y_{1}) = (1, 4)
(x_{2}, y_{2}) = (3, 9)
slope of a line
m =
m = = = 2.5 after toggle
slopeintercept b
b = y – mx
(x_{1}, y_{1}) or (x_{2}, y_{2}) can be used to calculate b; in this case, (x_{1}, y_{1}) = (1, 4) will be used:
slopeintercept b
b = y – mx = 4 – 2.5 × 1 = 1.5
slopeintercept form of the equation of a line
y = mx + b
y = 2.5x + 1.5
Input  Display  Comment 
blinker  clears screen  
9 – 4 3 – 1  m =  
2.5  m (Toggle) 

4 – 2.5 × 1  42.5*1  b = y – mx 
1.5  b  
SlopeIntercept

Question
Using the points (2, 3) and (4, 7) in the graph below, write the slopeintercept equation for Line L. The slope and yintercept should be in decimal form.
Answer
y = 2x – 1
Answer Process
(x_{1}, y_{1}) = (2, 3)
(x_{2}, y_{2}) = (4, 7)
slope of a line
m =
m = = = 2
slopeintercept b
b = y – mx
(x_{1}, y_{1}) or (x_{2}, y_{2}) can be used to calculate b; in this case, (x_{1}, y_{1}) = (2, 3) will be used:
b = y – mx = 3 – 2 × 2 = 1
slopeintercept form of the equation of a line
y = mx + b
y = 2x – 1
Input  Display  Comment 
blinker  clears screen  
7 – 3 4 – 2  m =  
2  m  
3 – 2 × 2  3 2* 2  b = y – mx 
1  b  
SlopeIntercept

Question
Without a graph, write the slopeintercept equation for the line passing through points (3, 7) and (5, 9.5). The slope and yintercept should be in decimal form.
Answer
y = 1.25x + 3.25
Answer Process
(x_{1}, y_{1}) = (3, 7)
(x_{2}, y_{2}) = (5, 9.5)
slope of a line
m =
m = = 1.25
slopeintercept b
b = y – mx
(x_{1}, y_{1}) or (x_{2}, y_{2}) can be used to calculate b; in this case, (x_{1}, y_{1}) = (3, 7) will be used:
b = y – mx = 7 – 1.25 × 3 = 3.25
slopeintercept form of the equation of a line
y = mx + b
y = 1.25x + 3.25
Input  Display  Comment 
blinker  clears screen  
9.5 – 7 5 – 3  m =  
1.25  m  
7 – 1.25 × 3  71.25*3  b = y – mx 
3.25  b  
SlopeIntercept

Question
Without a graph, write the slopeintercept equation for the line passing through points (3, 6) and (5, 8.5). The slope and yintercept should be in decimal form.
Answer
y = 1.25x + 2.25
Answer Process
(x_{1}, y_{1}) = (3, 6)
(x_{2}, y_{2}) = (5, 8.5)
slope of a line
m =
m = = 1.25
slopeintercept b
b = y – mx
(x_{1}, y_{1}) or (x_{2}, y_{2}) can be used to calculate b; in this case, (x_{1}, y_{1}) = (3, 6) will be used:
b = y – mx = 6 – 1.25 × 3 = 2.25
slopeintercept form of the equation of a line
y = mx + b
y = 1.25x + 2.25
Input  Display  Comment 
blinker  clears screen  
8.5 – 6 5 – 3  m =  
1.25  m  
6 – 1.25 × 3  6 1.25* 3  b = y – mx 
2.25  b  
SlopeIntercept

Question
The following table shows the age in years and height in inches of a boy and a girl.
Write the slopeintercept equation for the line passing through the boy’s growth points at (2, 34.00) and (4, 40.00).
Boy  Girl  
Age (yr)  Height (in)  Age (yr)  Height (in)  
2  34.00  2  33.50  
3  37.50  3  37.00  
4  40.00  4  39.50  
5  43.00  5  42.25  
6  45.25  6  45.00  
7  48.00  7  48.00  
8  50.25  8  50.00  
9  52.50  9  52.50  
10  54.50  10  54.25 
Answer
y = 3x + 28
Answer Process
(x_{1}, y_{1}) = (2, 34.00)
(x_{2}, y_{2}) = (4, 40.00)
slope of a line
m =
m = = 3
slopeintercept b
b = y – mx
(x_{1}, y_{1}) or (x_{2}, y_{2}) can be used to calculate b; in this case, (x_{1}, y_{1}) = (2, 34.00) will be used:
b = y – mx = 34.00 – 3 × 2 = 28
slopeintercept form of the equation of a line
y = mx + b
y = 3x + 28
Input  Display  Comment 
blinker  clears screen  
40.00 – 34.00 4 – 2  m =  
3  m  
34.00 – 3 × 2  34.003*2  b = y – mx 
28  b  
SlopeIntercept

Question
The following table shows the growth of an investment over time.
Time (years)  Value (dollars) 
2  100 
4  120 
6  140 
8  160 
10  180 
Based on the data in the table, which of the following slopeintercept equations represents the growth of an investment over time, where x is the year and y is the dollar value?
A. y = 10x + 80
B. y = 10x – 80
C. y = 10x – 80
D. y = 10x + 80
Answer
D. y = 10x + 80
Answer Process
Any two points in the data table will do; in this case, the following points will be used:
(x_{1}, y_{1}) = Point (2, 100)
(x_{2}, y_{2}) = Point (4, 120)
slope of a line
m =
m = = 10
slopeintercept b
b = y – mx
(x_{1}, y_{1}) or (x_{2}, y_{2}) can be used to calculate b; in this case, (x_{1}, y_{1}) = (2, 100) will be used:
b = y – mx = 100 – 10 × 2 = 80
slopeintercept form of the equation of a line
y = mx + b
y = 10x + 80
Input  Display  Comment 
blinker  clears screen  
120 – 100 4 – 2  m =  
10  m  
100 – 10 × 2  10010*2  b = y – mx 
80  b  
SlopeIntercept

Question
Bob planted some prairie grass to beautify a corner of his yard. After 3 weeks, the grass was 12 inches tall. After 7 weeks, the grass was 24 inches tall. If it grows at the same rate, how tall will the grass be at week 10?
Answer
33 inches
Answer Process
(x_{1}, y_{1}) = (3, 12)
(x_{2}, y_{2}) = (7, 24)
slope of a line
m =
m = = 3
slopeintercept b
b = y – mx
(x_{1}, y_{1}) or (x_{2}, y_{2}) can be used to calculate b; in this case, (x_{1}, y_{1}) = (3, 12) will be used:
b = y – mx = 12 – 3 × 3 = 3
slopeintercept form of the equation of a line
y = mx + b
y = 3x + 3
See PlugIn.
Plug in 10 for x.
y = 3 × 10 + 3 = 33
Input  Display  Comment 
blinker  clears screen  
24 – 12 7 – 3  m =  
3  m  
12 – 3 × 3  123*3  b = y – mx 
3  b  
3 × 10 + 3  3*10+3  y = mx + b Plug in 10 for x. 
33  Answer  
SlopeIntercept

Practice – Questions
1. Using the points (1, 6.5) and (2, 10) in the graph below, write the slopeintercept equation for Line L. The slope and yintercept should be in decimal form.
2. Without a graph, write the slopeintercept equation for the line passing through points (4, 8) and (8, 13). The slope and yintercept should be in decimal form.
3. The following table shows the age in years and height in inches of a boy and a girl.
Write the slopeintercept equation for the line passing through the girl’s growth points at (3, 37.00) and (7, 48.00). The slope and yintercept should be in decimal form.
Boy  Girl  
Age (yr)  Height (in)  Age (yr(  Height (in)  
2  34.00  2  33.50  
3  37.50  3  37.00  
4  40.00  4  39.50  
5  43.00  5  42.25  
6  45.25  6  45.00  
7  48.00  7  48.00  
8  50.25  8  50.00  
9  52.50  9  52.50  
10  54.50  10  54.25 
4. The following table shows the growth of an investment over time.
Time (years)  Value (dollars) 
3  250 
5  500 
7  750 
9  1000 
11  1250 
Based on the data in the table, which of the following slopeintercept equations represents the growth of an investment over time, where x is the year and y is the dollar value?
A. y = 125x – 125
B. y = 125x + 125
C. y = 125x – 125
D. y = 125x + 125
5. The following table shows the depreciation (loss in value) of an automobile over time.
Age (years)  Value (dollars) 
0  25000 
2  18000 
4  11000 
6  4000 
Based on the data in the table, which of the following slopeintercept equations represents the depreciation (loss in value) of an automobile over time, where x is the age in years and y is the dollar value?
A. y = 3500x – 25000
B. y = 3500x + 25000
C. y = 3500x – 25000
D. y = 3500x + 25000
6. Bob planted some prairie grass to beautify a corner of his yard. After 4 weeks, the grass was 18 inches tall. After 8 weeks, the grass was 48 inches tall. If it grows at the same rate, how tall will the grass be at week 12?
7. Betty sent 2 text messages at 4:00 AM and 7 text messages at 6:00 AM. If Betty increases her text message output at the same rate, how many texts will she send at 10 AM?
8. Bob spent $3.00 on popcorn at 5:00 PM and $4.50 on popcorn at 7:00 PM. If Bob increases his popcorn expenditures at the same rate, how much will he spend on popcorn at 10:00 PM?
9. The following table shows the approximate weight in kilograms (kg) over the first ten weeks of a pig’s life.
Age (weeks)  Weight (kg) 
0  1 
1  2 
2  3 
3  5 
4  8 
5  10 
6  15 
7  18 
8  20 
9  25 
10  30 
Using the table’s data points of (0, 1) and (2, 3), write a slopeintercept equation for the pig’s gain in weight, where x is the age in weeks and y is the weight in kg.
10. With reference to Question 9, use the table’s data points of (8, 20) and (10, 30) to write a slopeintercept equation for the pig’s gain in weight, where x is the age in weeks and y is the weight in kg.
Practice – Answers
1. y = 3.5x + 3
2. y = 1.25x + 3
3. y = 2.75x + 28.75
4. C. y = 125x – 125
5. B. y = 3500x + 25000
6. 78 inches
7. 17
8. $6.75
9. y = x + 1
10. y = 5x – 20