Applications of Linear Functions

Applications of Linear Functions

Miss Danes Design Algebra II TSAS

Open Ended

Question of the Day:

Snow, yay or nay?

Multiple Choice

Slope represents a rate of change. (Change in rise over change in run)

• True

• False

Multiple Choice

Which formula did the previous example use to solve?

• Slope Intercept form:

  $$y=mx+b$$

• Standard Form of a Line:

  $$Ax+By+C=0$$

• Slope Formula:

  $$\frac{y_{2\ }-y_1}{x_2-x_1}$$

• None of these

Multiple Choice

The population of a city increased from 23,400 in 2008 to 27,800 in 2012. Find the change of population per year if we assume the change was constant from 2008 to 2012.

• $$1,100\ \frac{year}{people}$$

• $$1,000\ \frac{year}{people}$$

• $$0.0009\ \frac{people}{year}$$

• $$1,100\ \frac{people}{year}$$

Marcus currently has 200 songs in his music collection. Every month he adds 15 new songs. Write a formula for the number of songs, N, in his collection as a function of time, t, the number of months. How many songs will he own in a year?

Multiple Choice

What was the function used to describe Marcus' song collection?

• $$N\left(t\right)=15t+200$$

• $$N\left(t\right)=200t+15$$

Fill in the Blanks

Using the information from the previous example. How many songs would Marcus have after 4 years?

Working as an insurance salesperson, Ilya earns a base salary plus a commission on each new policy. Therefore, Ilya’s weekly income, I, depends on the number of new policies, n, he sells during the week. Last week, he sold 3 new policies and earned $760 for the week. The week before, he sold 5 new policies and earned $920. Find an equation for I(n) and interpret the meaning of the components of the equation.

Multiple Choice

My first step is to use the slope formula $$m=\ \frac{y_{2\ }-y_1}{x_2-x_1}$$ to find the rate of cost per policy

How would I set that up?

• $$\frac{5-3}{920-760}\ \frac{policy}{dollar}$$

• $$\frac{920-5}{760-3}\ \frac{policy}{dollar}$$

• $$\frac{920-760}{5-3}\ \frac{dollar}{policy}$$

• None of these

Fill in the Blanks

Using the previous question's information

What is the rate?

Multiple Choice

To find the initial value (y - intercept) we will use the function $$I\left(t\right)=80n+b$$ and use one of our given ordered pairs, such as $$\left(760,\ 3\right)$$ and solve for $$b$$ .

Which is the correct set up?

• $$3=80\left(760\right)+b$$

• $$760=80\left(3\right)+b$$

• None of these

Fill in the Blanks

Using the formula from the previous question:

What is the initial value?

Multiple Choice

A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.

• c = 2.75b + 4

• c = 2.75b

• c =  4b- 2.75

• c = 2.75b - 4

Multiple Choice

Belinda's car needed repairs. The mechanic charged him $140 for the parts and an additional $48 an hour for labor. Write an equation that models this situation.

• y = 140x +48

• y = -48x +140

• y = 48x +140

• y = 48x

Multiple Choice

A man is climbing down from 100 feet high descending 30 feet per minute. Which function models his descent?

• y = 100 - 30x

• y = 100 + 30x

• y = 100x + 30

• y = 100x - 30

Multiple Choice

The equation below represents an elevator's height after an amount of seconds. Using this equation, what should the height of the elevator be after 14 seconds?
y = -3.8x + 290

• 80

• 236.8

• -80

• 72.6

Multiple Choice

What is the meaning of the slope in the context of the problem?

• It costs $3 for each book.

• The cost of 3 books.

• Each book costs $1.

• $1 for 3 books.

Multiple Choice

Derrick started a new job at McDonald's. He makes $10 per hour. Which graph models his total weekly earnings in terms of the number of hours he works?

Multiple Choice

Derrick started a new job at McDonald's. He makes $10 per hour. What is the independent variable?

• number of hours

• amount paid

Multiple Choice

Abby decides to get a magazine subscription. It costs her $2 per magazine plus an initial fee of $3. Define the variables

• y=the cost, x=the number of magazines

• y=the number of magazines, y=the cost