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Linear Functions as Mathematical Models (3.5). (a.k.a.: Word Problems) Aack, gaack, choke, cry. POD. What is the equation for the horizontal line passing through the point (2, -6)? What is the equation for the vertical line passing through the point (h, k)?. Classic Word Problem.

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linear functions as mathematical models 3 5

Linear Functions as Mathematical Models (3.5)

(a.k.a.: Word Problems)

Aack, gaack, choke, cry

slide2
POD

What is the equation for the horizontal line passing through the point (2, -6)?

What is the equation for the vertical line passing through the point (h, k)?

classic word problem
Classic Word Problem

’s Donuts

This place charges 55 cents each for a donut, plus a one-time charge of 20 cents for the box, the service, etc.

How would you figure out what x number of donuts cost?

Write down the steps you would take.

let s see if we can make this process standard for everyone
Let’s see if we can make this process standard for everyone

Share your steps with someone else in the class.

Let’s write on the board what we think as a class.

let s see if we can make this process standard for everyone1
Let’s see if we can make this process standard for everyone

The Method for Lines:

1. Read the problem carefully.

2. Identify the variables and their UNITS.

3. Decide which variable is independent and which is dependent.

4. How many points do you need to determine a line? Find them.

5. Determine an equation for the linear model.

6. Use that equation to answer the questions. Often this means to predict other points. Include UNITS in your answers!

try it
Try it

’s Donuts

This place charges 55 cents each for a donut, plus a one-time charge of 20 cents for the box, the service, etc.

a. Write an equation for the amount charged as a function of the number of donuts sold. (This is steps 1-5 of the Method.)

try it1
Try it

__________’s Donuts

This place charges 55 cents each for a donut, plus a one-time charge of 20 cents for the box, the service, etc.

b. Why is this a linear function? What does the slope represent? What does the y-intercept represent?

c. Predict the price of a box of a dozen donuts.

d. How many donuts would be a box priced at $4.05?

try it2
Try it

___’s Donuts

e. Sketch a graph of the function, using a reasonable domain. To do this,

1. Decide which variable for which axis.

2. Decide the intervals for each axis.

3. Plot the given and predicted points. Can you connect them?

4. Identify reasonable domains and ranges.

try it again
Try it again

Cricket Chirps

Based on information in Deep River Jim’s Wilderness Trailbook, the rate at which crickets chirp is a linear function of temperature. At 59°F they make 76 chirps per minute, and at 65°F they make 100 chirps per minute.

a. Write an equation expressing chirping rate as a function of temperature. (There’s a hint here– what is it?)

try it again1
Try it again

Cricket Chirps

b. Predict the chirping rate for 90°F.

c. How warm is it if you hear 120 chirps per minute?

d. Calculate the temperature intercept. What does this tell you about the real world?

e. Is there a temperature at which crickets will stop chirping?

try it3
Try it

You’ll do some of these in homework, of course.

The Method will come in very handy for this project.

I hope this is more exciting and more useful than simply writing stuff on a test.