# Understanding tables of values of linear relationships

### Understanding tables of values of linear relationships

Linear equations represent direct proportional relationships between x and y. A table of values contains the exact values of x and y. In this section, we will learn how to draw graphs based on the data from tables of values. From the tables and graphs, we will try to describe and determine whether the relationships are linear or not.
Basic Concepts: Ratios, Proportions

#### Lessons

• 1.
 x 4 5 6 7 8 y 21 28 35 42 49
a)
Draw a graph that shows the relationship between the values of x and y.

b)
Describe the relationship.

c)
Write an equation for x in relation to y.

• 2.
Is the relationship for each table of values linear? Explain and check your answer by graphing the values.
a)
 x y 3 - 9 4 -5 5 -1 6 3

b)
 a b 1 3 2 7 3 12 4 15

• 3.
Mary wants to rent a truck. The base rate of truck rental is $30, plus$2 per kilometre it travels.
a)
Write an equation for the cost of truck rental in relation to kilometre it travels.

b)
What is the cost at the moment when Mary picks up the truck?

c)
What is the cost if the truck travels 3.25 km?

d)
How far has the truck traveled if Mary is charged \$120?