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Using linear equations to solve word problems. Usually deal with changes over time. Y intercept does not change Slope does change .

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## Using linear equations to solve word problems

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**Using linear equations to solve word problems**Usually deal with changes over time.**Y intercept does not changeSlope does change**• Example: Kim wants to rent a car on the Big Island. Mr. Lee’s Rentals rents cars for $99.00 for one week plus $0.11 per mile over 100 miles. If Kim drives 400 miles, how much does she pay?**y=mx +/-b. y = .11x +99**• The weekly rental rate does not change. It is the y-intercept, and it’s $99.00. • The amount of miles changes, so it is the slope. The slope is the rate of change: $.11 per mile over 100 miles. • Let x = the number of miles she drives over 100 miles.**Example #2: y=5x+10**• Bobby charges $10. per lawn he mows, and an additional $5. per hour. • What does not change? What is the y-intercept? $10.00 per lawn • What changes? What is the slope? The $5. per hour depending on how many hours it takes to mow the lawn • Let x = the number of hours it takes to mow a lawn.**Create a My Way**• Make up a word problem where something is constant (does not change) and something does change. • State the y-intercept • State the slope • State what the variable (the “x”) is**Examples of Word Problems for My Way**• Cell Phone: $50. monthly rate + .12 cents a minute over 300 minutes. Let x = # of minutes over 300. • T-shirt company charges $24. per order plus $12.00 per shirt. Let x = the # of shirts ordered. Yoga classes: $10 for sign-up plus $5. per class**STEPS IN SOLVING WORD PROBLEMS WITH LINEAR ALGEBRA**• 1. Define the variable that you want to find with a let statement. Let x = …. • 2. Create an equation that expresses the information given in the problem’s scenario. Decide on the y-intercept and the slope (rate of change) • 3. Solve your equation using algebraic methods. • 4. Consider if your answer is reasonable. • 5. Label your solution appropriately. • 6. Check your answer with the conditions given in the problem.**Practice Problems**• Exercise #1: At a concert, Nabila purchased three t-shirts and a concert program that cost $15. In • total, Nabila spent $90. Find the cost of a single t-shirt if they all had the same price.

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