This answer key gives complete solutions for the independent and dependent variables worksheet. Each solution shows the equation, table, or graph reading used, and every final answer is in bold so students can check their work and axis labels.
Problem 1: Identifying Variables
- Independent: hours worked; dependent: money earned
- Independent: number of tickets; dependent: total cost
- Independent: miles driven; dependent: gas left
- Independent: age in weeks; dependent: height
Problem 2: Variables in Equations
- Independent: \(t\); dependent: \(d\)
- Independent: \(n\); dependent: \(c\)
- Independent: \(h\); dependent: \(p\)
- Independent: \(x\); dependent: \(y\)
Problem 3: Writing Equations
- \(c = 3n\)
- \(d = 55t\)
- \(p = 12h\)
- A square has 4 equal sides: \(P = 4s\)
Problem 4: Completing a Table
Multiply each \(n\) by \(4\): \(4\times 1 = 4\), \(4\times 2 = 8\), \(4\times 3 = 12\), \(4\times 4 = 16\), \(4\times 5 = 20\).
| \(n\) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \(c\) | 4 | 8 | 12 | 16 | 20 |
Problem 5: Table for an Addition Rule
Add \(6\) to each \(x\): \(0 + 6 = 6\), \(2 + 6 = 8\), \(4 + 6 = 10\), \(6 + 6 = 12\), \(8 + 6 = 14\).
Answer: \(y = 6, 8, 10, 12, 14\)
Problem 6: Plotting Points
Plot \((1, 4)\), \((2, 8)\), \((3, 12)\), \((4, 16)\), and \((5, 20)\).
The points lie on a straight line that rises as \(n\) increases; each step right of \(1\) goes up \(4\).
Problem 7: Equation from a Table
Each \(d\) is \(55\) times \(t\): \(55\times 1 = 55\), \(55\times 2 = 110\), \(55\times 3 = 165\), \(55\times 4 = 220\).
Equation: \(d = 55t\)
Problem 8: Reading a Graph
- Independent: time t; dependent: distance d
- At \(t = 3\), the graph is at \(9\): 9 miles
- At \(d = 6\), the graph is at \(t = 2\): 2 hours
- Each hour adds \(3\) miles, so \(d = 3t\)
Problem 9: Lemonade Stand
- Money equals $2 times cups: \(m = 2c\). The independent variable is \(c\).
- \(m = 2\times 12 = \) \(\$24\)
- \(30 = 2c\), so \(c = 30: 2 = \) 15 cups
Problem 10: Road Trip
- \(d = 65t\)
- \(d = 65\times 2.5 = 162.5\). Answer: 162.5 miles
- \(325 = 65t\), so \(t = 325: 65 = \) 5 hours
- The points are \((1, 65)\), \((2, 130)\), \((3, 195)\), \((4, 260)\), \((5, 325)\), \((6, 390)\). See graph.
See every chapter on the Grade 6 math page.