Using linear Using linear equations to solve equations to solve word problemsword problems

Usually deal with changes over time.Usually deal with changes over time.

Y intercept does not changeY intercept does not changeSlope does changeSlope does change

Example: Kim wants to rent a car on the Example: Kim wants to rent a car on the Big Island. Mr. Lee’s Rentals rents cars Big Island. Mr. Lee’s Rentals rents cars for $99.00 for one week plus $0.11 per for $99.00 for one week plus $0.11 per mile over 100 miles. If Kim drives 400 mile over 100 miles. If Kim drives 400 miles, how much does she pay? miles, how much does she pay?

y=mx +/-b. y = .11x y=mx +/-b. y = .11x +99+99

The weekly rental rate does not change. The weekly rental rate does not change. It is the y-intercept, and it’s $99.00.It is the y-intercept, and it’s $99.00.

The amount of miles changes, so it is the The amount of miles changes, so it is the slope. The slope is the rate of change: slope. The slope is the rate of change: $.11 per mile over 100 miles. $.11 per mile over 100 miles.

Let x = the number of miles she drives Let x = the number of miles she drives over 100 miles.over 100 miles.

Example #2: y=5x+10Example #2: y=5x+10

Bobby charges $10. per lawn he mows, and an Bobby charges $10. per lawn he mows, and an additional $5. per hour.additional $5. per hour.

What does not change? What is the y-What does not change? What is the y-intercept? $10.00 per lawnintercept? $10.00 per lawn

What changes? What is the slope? The $5. What changes? What is the slope? The $5. per hour depending on how many hours it per hour depending on how many hours it takes to mow the lawntakes to mow the lawn

Let x = the number of hours it takes to mow a Let x = the number of hours it takes to mow a lawn.lawn.

Create a My WayCreate a My Way

Make up a word problem where Make up a word problem where something is constant (does not change) something is constant (does not change) and something does change.and something does change.

State the y-interceptState the y-intercept State the slopeState the slope State what the variable (the “x”) isState what the variable (the “x”) is

Examples of Word Examples of Word Problems for My WayProblems for My Way

Cell Phone: $50. monthly rate + .12 Cell Phone: $50. monthly rate + .12 cents a minute over 300 minutes. Let x = cents a minute over 300 minutes. Let x = # of minutes over 300.# of minutes over 300.

T-shirt company charges $24. per order T-shirt company charges $24. per order plus $12.00 per shirt. Let x = the # of plus $12.00 per shirt. Let x = the # of shirts ordered.shirts ordered.

Yoga classes: $10 for sign-up plus $5. per Yoga classes: $10 for sign-up plus $5. per classclass

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 ProblemsPractice 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.