Slope refers to the Steepness of a Line
Basics
Slope refers to the steepness of a line.
Line 1 is steeper than Line 2.
Line 1’s slope is greater than Line 2’s slope.
A line is a flat straight figure extending infinitely through two points. (See Line L above.)
xaxis = horizontal
yaxis = vertical
x = horizontal coordinate
y = vertical coordinate
(x, y) = point representing horizontal and vertical coordinates on Line L
(o, b) = yintercept = point where Line L crosses the yaxis
m = slope
Formulas (Mathematics Formula Sheet)
slope of a line
m =
Formulas (NOT on Mathematics Formula Sheet)
slope as change
m =
Question
What is the slope of Line 1?
Answer
m = 2
Answer Process
slope as change
m =
m = = = 2
Question
What is the slope of Line 2?
Answer
m =
Answer Process
slope as change
m =
m = = =
Question
Using the points (3, 1) and (8, 3) in the graph below, calculate the slope of line L.
Answer
m =
Answer Process
(x_{1}, y_{1}) = (3, 1)
(x_{2}, y_{2}) = (8, 3)
slope of a line
m =
m = =
Input  Display  Comment 
blinker  clears screen  
3 – 1 8 – 3  m =  
Answer  
Slope 
Question
Express the previous answer in decimal form.
Answer
m = 0.4
Answer Process
See Toggle.
⇔ 0.4
Input  Display  Comment 
blinker  clears screen  
3 – 1 8 – 3  m =  
0.4  Answer (Toggle) 

Slope 
Question
Using the points (1, 2) and (4, 9) in the graph below, calculate the slope of line L in decimal form.
Answer
m = 2.333333333
Answer Process
(x_{1}, y_{1}) = (1, 2)
(x_{2}, y_{2}) = (4, 9)
slope of a line
m =
m = = = 2.333333333 after toggle
Input  Display  Comment 
blinker  clears screen  
9 – 2 4 – 1  m =  
2.333333333  Answer (Toggle) 

Slope 
Question
Round the previous answer to the nearest tenth.
Answer
m = 2.3
Answer Process
See Rounding.
2.333333333 → 2.3
Question
On the graph below, plot the points (2, 3) and (6, 9), draw a line through them, and calculate the slope of the line in decimal form.
Answer
m = 1.5
Answer Process
(x_{1}, y_{1}) = (2, 3)
(x_{2}, y_{2}) = (6, 9)
slope of a line
m =
m = = = 1.5 after toggle
Input  Display  Comment 
blinker  clears screen  
9 – 3 6 – 2  m =  
1.5  Answer (Toggle) 

Slope 
Question
On the graph below, plot the points (4, 1) and (10, 2) and calculate their slope in decimal form rounded to the nearest hundredth (without drawing a line).
Answer
m = 0.17
Answer Process
(x_{1}, y_{1}) = (4, 1)
(x_{2}, y_{2}) = (10, 2)
slope of a line
m =
m = = = 0.166666667 after toggle = 0.17 after rounding
Input  Display  Comment 
blinker  clears screen  
2 – 1 10 – 4  m =  
0.166666667  Answer (before rounding) 

Slope 
Question
On the graph below, plot the points (3, 2.5) and (7, 6.25) and calculate their slope in decimal form to the nearest hundredth (without drawing a line).
Answer
m = 0.94
Answer Process
(x_{1}, y_{1}) = (3, 2.5)
(x_{2}, y_{2}) = (7, 6.25)
slope of a line
m =
m = = 0.9375 =0.94 after rounding
Input  Display  Comment 
blinker  clears screen  
6.25 – 2.5 7 – 3  m =  
0.9375  Answer (before rounding) 

Slope 
Question
The following table shows the age in years and height in inches of a boy and a girl.
On the grid below the table, plot the xy coordinates for the boy at ages 2 and 8 and calculate their slope in decimal form to the nearest tenth (without drawing a line).
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
m = 2.7
Answer Process
(x_{1}, y_{1}) = (2, 34.00)
(x_{2}, y_{2}) = (8, 50.25)
slope of a line
m =
m = = 2.708333333= 2.7 after rounding
Input  Display  Comment 
blinker  clears screen  
50.25 – 34.00 8 – 2  m =  
2.708333333  Answer (before rounding) 

Slope 
Practice – Questions
1. What is the slope of Line 1?
2. What is the slope of Line 2?
3. Using the points (3.5, 1.5) and (7, 3.25) in the graph below, calculate the slope of line L.
4. On the graph below, plot the points (4, 1) and (8, 2), draw a line through them, and calculate the slope of the line in decimal form.
5. On the graph below, plot the points (1, 4) and (2, 8) and calculate their slope (without drawing a line).
6. The following table shows the age in years and height in inches of a boy and a girl.
On the grid below the table, plot the xy coordinates for the girl at ages 3 and 9 and calculate their slope in decimal form (without drawing a line).
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 
7. With reference to Question 6, express your answer as a fraction.
8. The following table shows the age in years and mileage for Car A and Car B.
On the grid below the table, plot the xy coordinates for Car A at years 3 and 6 and calculate their slope (without drawing a line).
Car A  Car B  
Age  Mileage  Age  Mileage  
1  10000  1  11000  
2  22000  2  20500  
3  33500  3  29725  
4  39000  4  41000  
5  48000  5  50500  
6  62000  6  58750  
7  71000  7  69900  
8  83250  8  81000  
9  90500  9  89900  
10  99500  10  99500 
9. The following table shows the age in years and mileage for Car A and Car B.
On the grid below the table, plot the xy coordinates for Car B at years 2 and 9 and calculate their slope (without drawing a line).
Car A  Car B  
Age  Mileage  Age  Mileage  
1  10000  1  11000  
2  22000  2  20500  
3  33500  3  29725  
4  39000  4  41000  
5  48000  5  50500  
6  62000  6  58750  
7  71000  7  69900  
8  83250  8  81000  
9  90500  9  89900  
10  99500  10  99500 
10. With reference to Question 9, round your answer to the nearest tenth.
Practice – Answers
1. m = 1
2. m = 2
3. m = 0.5
4. m = 0.25
5. m = 4
6. m = 2.583333333
7.
See Toggle.
8. m = 9500
9. m = 9914.285714
10. m = 9914.3