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Linear Functions Tables

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Linear Functions Tables

Use a rule to calculate outputs, complete tables and identify the constant change in a linear relationship.

Using function rules

For each table, apply the stated rule to every input.

1.Apply the rule y = 4x + 1 to complete the table.

Input x

Output y

2.When x increases by 1 in the rule y = 4x + 1, how much does y increase?

3.Use the rule y = 3x − 2 to fill in the missing outputs.

Input x

Output y

4.Describe the output pattern for y = 3x − 2 as the input goes up by 1.

Linear relationships in context

Use the information in each situation to write or complete a linear rule.

5.At a kite festival, Omar earns $6 for each kite he decorates. There is no starting payment. Complete the table for total earnings y after decorating x kites.

Kites x

Earnings y ($)

6.A kite is 12 cm above the ground when it begins rising. It gains 5 cm in height each second. Write a rule for its height h after t seconds, then find its height after 0, 1, 2 and 3 seconds.

Time t (s)

Height h (cm)

7.Which feature best describes a linear relationship?

The output changes by the same amount for each equal increase in input.
The output is always larger than the input.
The input and output must be equal.
The output changes by a different amount in every row.

8.A table has inputs 1, 2, 3, 4 and outputs 8, 11, 14, 17. Is this relationship linear? State the constant change in output.

9.For the rule y = 2x + 7, find y when x = 10.

10.A linear rule has an output of 4 when x = 0, and its output rises by 6 for every increase of 1 in x. Write the rule and find the output when x = 3.