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

Essential question: How do I create Essential question: How do I create and solve an equation to solve a and solve an equation to solve a word problem?word problem?

Review of Linear EquationsReview of Linear Equations

Remember that y = mx + bRemember that y = mx + b m is the slope (rise over run)m is the slope (rise over run) b is the y-interceptb is the y-intercept

STEPS IN SOLVING WORD PROBLEMS WITH LINEAR ALGEBRA

1. Find out what the total will be. Define the total as y. 2. What is the starting point or what doesn’t change.

This is the constant or y-intercept, b. 3. Decide what varies. Let this amount be x. 4. Decide if x is multiplied by an amount. This will be

the coefficient of x. 5. Plug what you know into the equation y = mx + b 6. Solve the problem 7. Make sure your solution is reasonable.

The y-intercept does not change, The y-intercept does not change, so it is the constant (no variable).so it is the constant (no variable).The slope goes with a value that The slope goes with a value that does change, so it is multiplied by does change, so it is multiplied by the variable x.the variable x.

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 for Big Island. Mr. Lee’s Rentals rents cars for $99.00 for one week plus $0.11 per mile. $99.00 for one week plus $0.11 per mile. If Kim drives 400 miles, how much does If Kim drives 400 miles, how much does she pay? she pay?

y=mx + b. y=mx + b.

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

STEPS IN SOLVING WORD PROBLEMS WITH LINEAR ALGEBRA

1. Find out what the total will be. Define the total as y. 2. What is the starting point or what doesn’t change. This is

the constant or y-intercept, b. $99 3. Decide what varies. Let this amount be x. 4. Decide if x is multiplied by an amount. This will be the

coefficient of x (the slope). .11 5. Plug what you know into the equation y = mx + b y = .11x + 99 6. Solve the problem. Plug in 400 miles for x y = .11(400) + 99 y = $143 7. Make sure your solution is reasonable.

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.

STEPS IN SOLVING WORD PROBLEMS WITH LINEAR ALGEBRA

1. Find out what the total will be. Define the total as y. 2. What is the starting point or what doesn’t change.

This is the constant or y-intercept, b. 3. Decide what varies. Let this amount be x. 4. Decide if x is multiplied by an amount. This will be

the coefficient of x. 5. Plug what you know into the equation y = mx + b 6. Solve the problem 7. Make sure your solution is reasonable.

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.