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Let's go through the questions one by one from this worksheet on linear relationships.

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### Solutions and Explanations

1. **Problem 9: Alexis' Phone Service**
   - **Given**: Activation fee = $50, monthly service fee = $20, duration = 3 months.
   - **Solution**: Total cost = Activation fee + (Monthly fee × Months) = 50 + (20 × 3) = 50 + 60 = $110.

2. **Problem 10: Percentage Calculation**
   - **Given**: Find 40% of 300.
   - **Solution**: $ 300 \times 0.4 = 120 $.

3. **Problems 11-13 (Using the Graph)**
   - **11. Starting Salary**: From the graph, Kendra’s starting salary is $15,000.
   - **12. Annual Salary Increase**: Based on the graph, her salary increases by $5,000 each year.
   - **13. Equation of the Relationship**:
     - **Solution**: $ y = 5000x + 15000 $ where $ y $ is Kendra’s salary and $ x $ is the number of years worked.

4. **Problem 14: Probability of Rolling a 2 or 4**
   - **Given**: Fair number cube (like a die), numbers 1-6.
   - **Solution**: Probability = $ \frac{2}{6} = \frac{1}{3} $.

5. **Problem 15: Cost of Apples**
   - **Table Analysis**: Notice the cost per apple rises linearly as more apples are bought.
   - **Pattern**: Price increases by $0.50 per apple.

6. **Problem 16: Kathy's Driving Rate**
   - **Given**: Distance = 100 miles, Time = 2 hours.
   - **Solution**: Rate = $ \frac{100 \text{ miles}}{2 \text{ hours}} = 50 $ miles per hour.

7. **Problem 17: Cost of Movie Tickets**
   - **Given**: Costs for different numbers of tickets in a table.
   - **Solution**: Each ticket costs $ \frac{18}{2} = 9 $ dollars.

8. **Problem 18: Solving the Linear Equation**
   - **Equation**: $ y = 2x + 3 $.
   - **When $ x = 5 $**: $ y = 2(5) + 3 = 10 + 3 = 13 $.

9. **Problem 19: Deshawn's Earnings**
   - **Given**: Earns $10 per hour.
   - **Answer**: Equation for total weekly earnings if he works $ h $ hours: $ 10h $.

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Would you like more details on any of these solutions or explanations?

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### Related Questions

1. How would the answer change if Alexis used her phone for a different number of months?
2. What is the formula for finding any percentage of a given number?
3. If Kendra received a different starting salary, how would the equation change?
4. What is the probability of rolling an odd number on a fair cube?
5. Can the pattern in Problem 15 be considered a linear relationship?

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### Tip

When analyzing patterns in a table, try calculating the difference between terms to identify whether it's a linear or non-linear relationship.

Math worksheet on linear relationships covering problems related to percentage calculations, interpreting graphs, probability, analyzing patterns, and solving linear equations.

Explore solutions for a worksheet on linear relationships for Grades 5-7, including problems on percentages, graph interpretation, probability, patterns, and linear equations.

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