These 10 problems practice identifying independent and dependent variables and relating them with equations, tables, and graphs from Common Core 6.EE.C.9. You write equations such as \(d = 65t\), complete tables, plot points, and read values from a graph.
Problems 8 through 10 are word problems about a hike, a lemonade stand, and a road trip. Label every axis with the quantity it shows.
Problem 1: Identifying Variables
Name the independent variable and the dependent variable in each situation.
- The number of hours Ethan works and the money he earns
- The number of tickets bought and the total cost
- The miles Liam drives and the gas left in the tank
- A sunflower’s age in weeks and its height
Problem 2: Variables in Equations
Name the independent variable and the dependent variable in each equation.
- \(d = 65t\)
- \(c = 3n\)
- \(p = 12h\)
- \(y = x + 4\)
Problem 3: Writing Equations
Write an equation for each situation.
- The cost \(c\) of \(n\) notebooks that cost $3 each
- The distance \(d\) after \(t\) hours at \(55\) miles per hour
- The pay \(p\) for \(h\) hours at $12 per hour
- The perimeter \(P\) of a square with side length \(s\)
Problem 4: Completing a Table
Complete the table for the equation \(c = 4n\).
| \(n\) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \(c\) | ___ | ___ | ___ | ___ | ___ |
Problem 5: Table for an Addition Rule
Complete the table for the equation \(y = x + 6\).
| \(x\) | 0 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|
| \(y\) | ___ | ___ | ___ | ___ | ___ |
Problem 6: Plotting Points
Plot the points from the table for \(c = 4n\) on the grid, with \(n\) on the horizontal axis and \(c\) on the vertical axis. Then describe the pattern the points make.
Problem 7: Equation from a Table
Write an equation for the table, with t as the independent variable and d as the dependent variable.
| \(t\) (hours) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| \(d\) (miles) | 55 | 110 | 165 | 220 |
Problem 8: Reading a Graph
The graph shows the distance d, in miles, that a hiker walks in t hours.
- Name the independent and dependent variables.
- How far does the hiker walk in 3 hours?
- How many hours does it take to walk 6 miles?
- Write an equation relating d and t.
Problem 9: Lemonade Stand
At the Little League snack stand, Sofia sells lemonade for $2 per cup. Let \(c\) be the number of cups sold and \(m\) the money collected in dollars.
- Write an equation and name the independent variable.
- Find the money collected when 12 cups are sold.
- Find the number of cups sold when the money collected is $30.
Problem 10: Road Trip
Aisha’s family drives at a steady \(65\) miles per hour. Let \(t\) be the time in hours and \(d\) the distance in miles.
- Write an equation for d in terms of t.
- Find the distance after 2.5 hours.
- Find the time to drive 325 miles.
- Plot the points for \(t = 1, 2, 3, 4, 5, 6\) hours on the grid.
See every chapter on the Grade 6 math page.