LINEAR MODEL WORD PROBLEMS WORKSHEET

Problem 1 :

The table show the number of inches of snow on the ground as a function of time afternoon.

a)  What is the initial value of the function ?

b)  What does the value represent ?

c)  What is the rate of change of the function in the Example? What does this value represent?

Solution :

a) The initial value = 6

b)  Meaning : At noon 12 pm, the height of the snow is 6 inches.

c) Finding rate of change :

(0, 6) and (1, 8.5)

m = (y₂ - y₁) / (x₂ - x₁)

m = (8.5 - 6) / (1 - 0)

m = 2.5

Every hour the height snow is increasing by 2.5 feet.

Problem 2 :

The graph shows money in dollars as a function of time in days. White an equation for the function, and describe a situation that it could represent. Include the initial value, rate of change, and what each quantity represents in the situation.

a)  Equation of the function (y = mx + b) and what situation it represents

b)  Initial Value Rate of Change

c)  x” represents

d)  “y” represents

Solution :

a) Taking two points on the straight line, (0, 25) and (10, 125)

Rate of change = (125 - 25)/(10 - 0)

 = 100/10

= 10

y-intercept = 25

Equation of the line :

y = mx + b

y = 10x + 25

b)  To figure out the initial value, we have to apply the value x as 0.

y = 10(0) + 25

y = 25

So, the initial value is 25 days.

c)  x represents, the number of days

d)  y represents, the amount in dollars.

Problem 3 :

Each day Kyle buys a cup of soup and a salad for lunch. The salad costs a certain amount per ounce. The equation below models the total cost of Kyle’s lunch.

y = 0.45x + 3.75

a) What do the variables x and y represent? Use the phrase is a function of to describe how the equation relates these quantities to one another.

b) What does the value of the function for x = 0 represent?

c) What does the rate of change represent?

d)  What is the cost of an 8-ounce salad without soup? How do you know?

Solution :

y = 0.45x + 3.75

Here 3.75 is the cost of cup of soup

0.45 represent cos of salad per ounce.

x - number of ounce of salad she is ordering.

y - be the total cost she is spending for lunch.

a) based on number of ounces of salad she is ordering, she has to spend more money for lunch.

b)  y = 0.45x + 3.75

When x = 0

y = 0.45(0) + 3.75

y = 3.75

c) The rate of change will represent the number of ounce of salad increases, the amount she is spending for lunch will also increase.

d)  y = 0.45x + 3.75

When x = 8

y = 0.45(8) + 3.75

y = 3.6 + 3.75

y = 7.35

Problem 4 :

Carmela is a member of a social club. She pays an annual membership fee and $15 for each event she attends. The equation y = 15x + 25 represents her total cost each year. Which statement(s) about the function is true?

A. The initial value is 15.

B. x represents the cost of each event.

C. The rate of change is 15.

D. The initial value represents the annual membership fee.

E. The number of events she attends is a function of the total cost.

F. The total cost is a function of the number of events she attends.

Solution :

y = 15x + 25

Comparing the given equation with y = mx + b

slope = rate of change = 15 and y-intercept = 25

Charge for each event she attends = 15

membership fee = 25

So, B, C and D are correct.

Problem 5 :

Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase for different number of tickets in the table shown.

a) What is the equation that models this linear function? 

b) How much is each movie ticket?

c) How much is the convenience?

Solution :

Rate of change m = (y₂ - y₁) / (x₂ - x₁)

= (44.50 - 32)/(3 - 2)

= 12.5

y = mx + b

y = 12.5x + b ----(1)

Rate of change (m) = 12.5, to figure out the initial value, let us apply one of the point in the equation.

82 = 12.5(6) + b

b = 82 - 75

b = 7

Applying the value of b in (1), we get

y = 12.5x + 7

b) Each ticket cost 12.5