Rate of Change and Modeling Practical Situations

Rate of Change (LT 3.6)

​I can interpret slope as rate of change for practical purposes.

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• ​Find slope of the line

• ​Interpret the correct way to divide to find rate of change.

​Notes:

• ​The rate of change is basically the SAME thing as the slope. ​It's calculated the same way:

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• ​The difference? The rate of change will have UNITS (label)

Multiple Choice

Which of the following are ways to find the rate of change?

• change in y over

  change in x

  $$\frac{\Delta y}{\Delta x}$$  

• rise over run
• all option

• $$\frac{y_2-y_1}{x_2-x_1}$$  

Multiple Choice

What is the rate of change for the following graph?

• 80 mi/hr

• 80 hr/mi

• 40 mi/hr

• 40 hr/mi

Multiple Choice

Find the rate of change between the points (-2 , 10) & (4 , 14); x in minutes, and y in feet

• rises

  .66 feet/minute

• falls

  1.5 feet/minute

• rises

  1.5 feet/minute

• falls

  .66 feet/minute

​Using Rate of Change and Intial Value

M - Rate of Change

​B - Initial Value

​X - # of items, time

​Y - total cost, total number, total....whatever!

Multiple Choice

When a tow truck is called, the cost of the service is $10 plus $1 per mile that the car must be towed. Write a linear equation to represent the total cost of the towing service.

• y= 10x +1

• y= x +10

• y= -10x + 1

• y= -x +10

Multiple Choice

Your new job is at the Custom T- Shop, where T-shirts are printed to order. For each order, Custom T Shop, charges $8.00 per shirt plus a one time set up fee of $15.00. Write a linear equation to show the relationship.

• y= -8x + 15

• y= 15x + 8

• y= -15x + 8

• y= 8x +15

Multiple Choice

When a plumber is called, the cost of the service call is $50 for him to show up at your house, plus an additional $25 per hour. Write a linear equation.

• y=50x + 25

• y= 25x + 50

• y= -25x - 50

• y= -50x -25

Multiple Choice

Your cell phone company charges $20 a month plus $0.50 per text message. Write an equation to show the total cost the cell phone company charges.

• y= 20x + .50

• y= -0.50x + 20

• y= 0.50x + 20

• y= -20x - 0.50

Multiple Choice

Suppose a town has a population of 5,000 residents but that the population is decreasing by 200 people each year. Write a linear equation for this situation.

• y= -200x + 5000

• y= -5000x + 200

• y= 200x + 5000

• y= 5000x+ 200

Multiple Choice

At a fair, Bob draws caricatures. He pays the fair $30 for the space to set up a table and $2 for each drawing he sells. Write a linear equation to show how much he pays total.

• y= 2x -30

• y= 2x + 30

• y= 30x + 2

• y= -2x + 30

Multiple Choice

The rental rate at Rent a Wreck is $30 per day plus $0.25 per mile driven. Write a linear equation to find the total cost for each day.

• y= 30x + .25

• y= -0.25x- 30

• y= 0.25x + 30

• y= -30x- 0.25

Multiple Choice

Mike is buying a large pizza. The pizza cost $8.00 plus $0.50 for each additional topping. Which function correctly models the situation?

• y= 8x +.50

• y= 8.50x

• y= .50x+ 8

• y= 8x- .50x

Multiple Choice

Bob the plumber charges $15 per hour plus a service fee of $40 for coming out to your house. Which function models this situation?

• y= 40x+ 15

• y= 15x- 40

• y= 15x

• y= 15x + 40

Multiple Choice

Valerie is traveling at a rate of 65mph. Which function would be used to model the situation?

• y= 65x

• y= x

• y= x + 65

• y= 65

Multiple Choice

Thomas got a speeding ticket. The cop said he has to pay $10 per hour he was going over the speed limit. Plus Thomas has to pay $115 court cost. Which equation models what Thomas would have to pay?

• y= 10x + 115

• y= 115x+ 10

• y= 125x

• y= 10x- 115

Multiple Choice

A business purchases a computer for $1500. The computer goes down in value $200 each year when the new model is released. Write a function to model the situation.

• y= 1500x- 200

• y= 200x- 1500

• y= 200x + 1500

• y= -200x + 1500

Multiple Choice

There were approximately 11,000 students enrolled at Western Carolina last year. This figure goes up about 225 each year. Write a function to model this situation.

• y= -225x+ 11000

• y= 225x+ 11000

• y= 225x- 11000

• y= 11000x+ 225

Multiple Choice

Ted's Taxi service charges a $5 pick up fee plus $2 per mile. Which function describes the situation

• y= 2x+5

• y= 2x- 5

• y= 5x+ 2

• y= 5x- 2

Multiple Choice

Alan buys a new car for $25,000. It depreciates at a rate of $2000 per year. Which function can be used to find the value after x years?

• y= 25000- x

• y= 2000x- 25000

• y= -2000x+ 25000

• y= 25000x- 2000