Dependent and Independent Variables: math practice, Grade 6

Rate this post

Math practice Grade 6 : Dependent and Independent Variables — Zyro the alien explorer of Planète Maths

22 problems graded by difficulty (★ easy, ★★ medium, ★★★ hard). Try first, without looking at the solutions!

1 Name the variables ★★★

For each situation, name the independent variable and the dependent variable.

The number of minutes on a treadmill and the calories burned.
The number of pizzas ordered and the total price.
The amount of rain that falls and the water level in a rain barrel.

2 Complete the table ★★★

The rule is \( y = 4x \). Copy and complete the table.

\( x \)	1	2	3	4	5
\( y \)	?	?	?	?	?

3 Movie tickets ★★★

A movie ticket costs 9 dollars. Let \( t \) be the number of tickets and \( c \) the total cost in dollars.

Write an equation for \( c \).
How much do 6 tickets cost?
A group spends 117 dollars. How many tickets did they buy?

4 Use the rule ★★★

The rule is \( y = x + 7 \). Find \( y \) when \( x = 3 \), \( x = 8 \) and \( x = 15 \).

5 From a table to ordered pairs ★★★

Write the table below as ordered pairs. Which variable goes first in each pair, and on which axis would you place it?

Hours \( h \)	1	2	3
Pages read \( p \)	2	4	6

6 True or false? ★★★

Decide whether each statement is true or false, and explain.

In the equation \( d = 5t \), the variable \( d \) is independent.
For \( y = 5x \), the ordered pair \( (4, 20) \) has the independent value first.
In a graph, the independent variable is usually on the horizontal axis.
For \( y = x + 3 \), when \( x = 18 \) we get \( y = 6 \).

7 Growing bamboo ★★★

A bamboo shoot grows 2 inches each day. Let \( d \) be the number of days and \( h \) the growth in inches.

Make a table for \( d = 1 \) to \( 5 \).
Write the rule.
How much has it grown after 7 days? Give the answer in inches and in centimeters (1 inch = 2.54 cm).

8 Find the rule: adding ★★★

Find the rule for the table, then use it to find \( y \) when \( x = 40 \).

\( x \)	2	3	4	5
\( y \)	9	10	11	12

9 Find the rule: multiplying ★★★

Find the rule for the table. Then find \( y \) when \( x = 10 \), and \( x \) when \( y = 96 \).

\( x \)	1	2	3	4
\( y \)	6	12	18	24

10 Reading a graph ★★★

Maya saves the same amount of money each week. The graph shows her savings \( s \) in dollars after \( w \) weeks.

Which variable is independent? Which is dependent?
How much does she save each week?
Write an equation for \( s \).
How much will she have saved after 8 weeks?

11 Cousins ★★★

Leo is 4 years older than his cousin. Let \( a \) be the cousin’s age and \( L \) Leo’s age.

Write a rule for \( L \).
Complete a table for \( a = 6, 9, 12 \).
How old is the cousin when Leo is 20?
Is the ratio \( L : a \) the same for every pair? Explain.

12 The jogger ★★★

A jogger runs at a steady pace.

Minutes \( m \)	5	10	15	20
Miles \( d \)	0.5	1	1.5	2

What is the constant rate of change?
Write an equation.
How far does she run in 45 minutes?

13 Is the rate constant? ★★★

The table shows the cost \( c \) in dollars of \( n \) packs of stickers at a store.

\( n \)	1	2	3	4
\( c \)	3	6	10	15

Is the rate of change constant? Can the relationship be written as \( c = kn \)? Explain.

14 Trail mix ratio ★★★

A trail mix has 3 cups of raisins for every 2 cups of nuts. Let \( n \) be the cups of nuts and \( r \) the cups of raisins.

Complete the table.
Write the pairs \( (n, r) \).
Will the graph be a line through the origin? Why?
How many cups of raisins go with 10 cups of nuts?

\( n \)	2	4	6	8
\( r \)	3	?	?	?

15 Taxi fare ★★★

A taxi charges a pickup fee of 3 dollars plus 2 dollars for each mile. Let \( m \) be the number of miles and \( c \) the cost in dollars.

Write an equation for \( c \).
Make a table for \( m = 0 \) to \( 5 \).
What is the rate of change?
A ride costs 25 dollars. How long was it?

16 Two cyclists ★★★

The graph shows the distance \( d \) in miles covered by Ana and Ben as functions of the time \( t \) in hours. Both ride at a steady pace.

Who rides faster? How can you tell from the graph?
Write an equation for each cyclist.
What is the difference between their distances after 3 hours?
After how many hours is Ana 12 miles ahead?

17 Find the mistake ★★★

A student looks at this table and writes the rule \( y = x + 3 \).

\( x \)	1	2	3
\( y \)	4	8	12

Explain what is wrong and give the correct rule. Then find \( y \) when \( x = 25 \).

18 The printer ★★★

A printer prints 18 pages per minute. Let \( m \) be the number of minutes and \( p \) the number of pages.

Write an equation.
How many pages in 10 minutes?
How long does it take to print 135 pages?
Is \( m \) or \( p \) the independent variable? Explain.

19 A line that misses the origin ★★★

The graph shows the rule \( y = x + 4 \).

Read the ordered pair for \( x = 0 \). Why does this matter?
What is the rate of change?
Is the ratio \( y : x \) constant? Test \( x = 1 \) and \( x = 4 \).
Explain why this line is not like the graph of a constant ratio.

20 Your own situation ★★★

Invent a real-world situation with a constant rate of 6 items per box. Name the independent and dependent variables, write an equation, and make a table with four values.

21 A road trip ★★★

A family drives at a constant speed of 55 miles per hour. Let \( t \) be the hours and \( d \) the distance in miles.

Write an equation.
How far do they drive in 3.5 hours?
How long to drive 330 miles?
Express the speed in kilometers per hour (1 mile \( \approx \) 1.609 km), rounded to the nearest tenth.