PROBLEMS ON INTERPRETING LINEAR FUNCTIONS

Problem 1 :

The drone in the Example hovers at 16 meters for a few minutes before being lowered at constant rate. It reaches the ground after 6 seconds.

a. Why can the drone's descent be modeled by a linear function?

b. The linear model of the drone's descent gives its height a function of time. Is the rate of change positive or negative?

c. What equation models the drone's descent as time increases? 

Solution:

a)

y = kx + b (k is a constant value)

D = vt (Distance = speed × time)

The speed is constant.

The drone's descent be modeled by a linear function.

b) The distance from the drone to the ground is decreasing, then k < 0.

The rate of change is negative.

c) 

y = kx + 16

y represents the distance from the drone to the ground x represents time.

x = 6, y = 0

6k + 16 = 0

6k = -16

k = -8/3

y = -8/3x + 16

Problem 2 :

The Drama Club is selling tie-dye T-shirts as a fundraiser. They buy the dyeing materials for $60 and white T-shirts for $2.50 each. They sell the finished shirts for $10 each.

a. Write an equation for the money they spend y, as a function of the number of T-shirts they buy, x.

b. Write an equation for the money they collect, y, as a function of the number of T-shirts they sell, x.

c. Write an equation for their profit, y, as a function of the number of T-shirts they sell, x.

Solution:

a)

y = 2.5x + 60

b)

y = 10x

c) 

y = 10x - (2.5x + 60)

profit = sell - cost

y = 7.5x - 60

Problem 3 :

On his first birthday, Tomas was 30 inches tall. For the next year, he grew half an inch each month. What equation models his height during that year, y, as a function of the number of months, x.

Solution:

y = mx + b

y is his height during that year

x is the number of months

m is the slope or rate of change, which is 1/2 inch every month

b is the y-intercept, which is 30 inches. So

y = 1/2x + 30

Problem 4 :

Which savings plan can be modeled by y = 50x + 25? (choose one)

a. Start with $50. Save $25 each week.

b. Save $250 in 5 weeks for a total of $300.

c. Start with $25. The total saved after 5 weeks is $275.

d. The total saved is $25 the first week and $50 the second week.

Solution:

a) 

y = 50x + 25

b)

Slope = 50

y- intercept = 25

c) 

Start with $25, when x = 5.

y = 50 × 5 + 25

y = 275

Start with $25, the total saved after 5 weeks is $275.

Problem 5 :

The equation y = 0.15x + 0.40 represents the cost of mailing a letter weighing 1 ounce or more. In the equation x, represents the weight of the letter in ounces and y represents the cost in dollars of mailing the letter.

Fill in the blank:

a) In this situation, the _____ is a function of the  _____.

b) What is the cost of mailing a letter that weighs 3 ounces?

Solution:

a)  Cost in dollars of mailing the letter is the function of weight of letter.

y = 0.15x + 0.40

b) Cost of mailing letter, when the weight of the letter is 3 ounces,.

x = 3, y = ?

y = 0.15(3) + 0.40

y = 0.45 + 0.40

y = 0.85

So, cost of mailing 3 ounces letter is $0.85.