# Lesson 14Using Linear Relations to Solve Problems

Let’s write equations for real-world situations and think about their solutions.

### Learning Targets:

- I can write linear equations to reason about real-world situations.

## 14.1 Buying Fruit

For each relationship described, write an equation to represent the relationship.

- Grapes cost $2.39 per pound. Bananas cost $0.59 per pound. You have $15 to spend on pounds of grapes and pounds of bananas.
- A savings account has $50 in it at the start of the year and $20 is deposited each week. After weeks, there are dollars in the account.

## 14.2 Five Savings Accounts

Each line represents one person’s weekly savings account balance from the start of the year.

- Choose one line and write a description of what happens to that person's account over the first 17 weeks of the year. Do not tell your group which line you chose.
- Share your story with your group and see if anyone can guess your line.
- Write an equation for each line on the graph. What do the slope, , and vertical intercept, , in each equation mean in the situation?
- For which equation is a solution? Interpret this solution in terms of your story.
- Predict the balance in each account after 20 weeks.

## 14.3 Fabulous Fish

The Fabulous Fish Market orders tilapia, which costs $3 per pound, and salmon, which costs $5 per pound. The market budgets $210 to spend on this order each day.

- What are five different combinations of salmon and tilapia that the market can order?
- Define variables and write an equation representing the relationship between the amount of each fish bought and how much the market spends.
- Sketch a graph of the relationship. Label your axes.
- On your graph, plot and label the combinations A—F.
A B C D E F pounds of tilapia 5 19 27 25 65 55 pounds of salmon 36 30.6 25 27 6 4 - Which of these combinations can the market order? Explain or show your reasoning.

- List two ways you can tell if a pair of numbers is a solution to an equation.

## Lesson 14 Practice Problems

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120.

- Describe some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers. Explain how you found them.
- Write an equation to represent the situation. What do the variables represent?
- Create a graph to represent the situation.
- What does the slope tell us about the situation?
- Interpret the and intercepts in the situation.

Triangle is an isosceles triangle with two angles of measure degrees and one angle of measure degrees.

- Find three combinations of and that make this sentence true.
- Write an equation relating and .
- If you were to sketch the graph of this linear equation, what would its slope be? How can you interpret the slope in the context of the triangle?

Select

**all**the equations for which is a solution.Consider the following graphs of linear equations. Decide which line has a positive slope, and which has a negative slope. Then calculate each line’s exact slope.