Name: ___________________________ Class: ___________________
Linear Relations Practice
1. Make a table of values that for the first six figures comparing the
figure number and the number of squares.
Write a linear equation that represents the relationship between the
figure number and the number of squares.
2. Make a table of values that for the first six tables comparing the
number of tables and the number of people that can sit.
Write a linear equation that represents the relationship between the
number of tables and the number of people that can sit.
a. I called Kelly’s cab for a ride home. The cost of the ride is shown.
Complete the table of values for the given distance.
Number
of km
10
15
b. Write an linear equation that relates the fare to the distance
travelled.
20
25
30
c. How far did you travel if the cost was $123.60?
Cost $
3. An airplane is cruising at a height of 10 000 m. It descends to land.
Tis table shows the height of the plane every minute after it began
its decent.
a. Write an linear equation that relates the height of the plane to the
time since it began its decent.
b. What is the height of the plane after 15 minutes?
c. How long after beginning its decent does the plane land?
4. Write a linear equation that represents the relationship between t and v.
5. Hexagonal tables are arranged as shown. The pattern continues. One person sits at each side of the
table. Create a table of values comparing the number of tables and the number of people that can be seated in
each rragement.
a. Write an equation that related the number of people who can be
seated at a table.
b. How many tables are needed to seat 41 people?
6. The cost to print brochures is the sum of a fixed cost of $250 plus $1.25 per brochure.
a. Write an equation that relates the total cost, c, to the number of brochures, n.
b. What is the cost of printing 2500 brochures?
c. How many borchures can be printed for $625?
7. You open a savings account. The initial balance is $315.00. You deposit $15 per week for a year.
a. Create a table of values that represents the balance of the bank
account for the first five deposits
b. Write an equation to model this situation.
c. How long will it take you to save $500?
8. A number pattern starts at 4.5. Each number after that is 5.5 more than the previous number.
a. Make a table of values for the first five terms.
b. Develop an equation that can be used to determine the value of
each term in the pattern.
c. What is the value of the 32nd term?
d. Which term has a value of 664.5?
9. Tree planters are paid a flat rate of $11.00 per hour plus $1.75 per each tree that they plant.
a. Write an equation to relating the number of trees planted and the
Trees Planted Dollars Earned
dollars earned per hour.
0
10
20
30
b. Make a table of values comparing the number of trees planted and
dollars earned per hour.
40
10. Write the linear equation that is represented by each table of values. Fill in the missing pieces of
information.
x
y
x
y
x
y
1
4
1
3
1
2.5
2
9
2
0
2
5.7
3
14
3
-3
3
8.9
4
19
4
-6
4
5
7
13
x
y
w
1
-8.4
1
2
-3.7
2
3
1
3
50.5
z
x
1
2
-12.2
4
4
-15.6
10
5
-19
3
4
y
1
4
1
1
1
4
1
5
2
3
5
-66.6
 14
1
2
11. Which of the following expressions represents the relationship between figure number and number of
squares?
a) 5 f
b) 2 f
c) 5  f
d) 5  s
12. This pattern of sqaures continues. Which equation below relates the number of sqaures, n, in a picture
to the number size, s?
a) n  s  4
b) n  4s  1
13. Look at the graphs to answer each question:
c) n  4s
d) s  4n
a. What is the approximate value of d when h = 2.5?
b. What is the approximate value of h when d = 250?
c. What is the approximate value d when h = 3.75?
d. What is the approximate value of y when x = 3.5?
e. What is the approximate value of x when y = 0.5?
f. What is the approximate value of y when x = -4?
14. A gym charges a $3.75 flat rate to enter the rec center. In addition to the flat rate, it costs $1.65 per hour
to use the pool.
a. Create a table of values illustrating the number of hours in the pool and the cost.
b. Write a linear equation illustrating the relationship.
c. Graph the linear relation.
15. Identify which of the following graphs and tables of values represent a linear relation. Justify your answer.
Graph
Linear Relation?
Justify your answer.
16. Write an equation that represents each graph.
Table of Values
Linear Relation?
Justify your answer.
17. Create a table of values for each linear relation. Using values -2 to 2.
a. y  3x
b. 2 x  7  y
c.
 4x  3  y
18. Each table of values represents a linear relation. Complete the table of values:
19. Does each equation describe a vertical line, a horizontal line, or an oblique line?
Equation
y7
Vertical, Horizontal or
Oblique Line
Equation
y  3x  3
x  5
y  6  2x
yx
x y3
x90
x
1
4
Vertical, Horizontal or
Oblique Line
20. Match each graph on the grid with its equation.
i.
yx
y  2x
ii.
iii.
y  3 x
21. Match each graph with its linear equation.
a.
i.
b.
y  2x  1
ii.
c.
y  2x  5
iii.
y  2x  3
22. Match the graph with its linear equation.
i.
y  3x  3
ii.
x y 3
iii.
y  3x  3