8th grade Ch 4 L6

As part of a grand opening, an arcade gave out free tokens to the first 100 customers. The graph shows the number of tokens customers received for each dollar spent at the Play More Arcade. Find and interpret rate of change and the initial value.

• Rate of change: 8 tokens per dollar; Initial value: 12 tokens (from the y-intercept of the graph)

• Rate of change: 12 tokens per dollar; Initial value: 8 tokens (from the y-intercept of the graph)

• Rate of change: 10 tokens per dollar; Initial value: 0 tokens (from the y-intercept of the graph)

• Rate of change: 5 tokens per dollar; Initial value: 20 tokens (from the y-intercept of the graph)

• Rate of change: $2 per hour; Initial value: $4 (rental fee)

• Rate of change: $3 per hour; Initial value: $2 (rental fee)

• Rate of change: $4 per hour; Initial value: $2 (rental fee)

• Rate of change: $2 per hour; Initial value: $2 (rental fee)

A science center charges an initial membership fee. The total cost of the membership depends on the number of people on the membership as shown in the table. Assume the relationship between the two quantities is linear. Find and interpret the rate of change and the initial value.

• Rate of change: $15 per person; Initial value: $35 (membership fee)

• Rate of change: $35 per person; Initial value: $15 (membership fee)

• Rate of change: $20 per person; Initial value: $30 (membership fee)

• Rate of change: $10 per person; Initial value: $40 (membership fee)

How is the initial value of a function represented in a table and in a graph?

• In a table, the initial value is the output when the input is zero. In a graph, the initial value is the y-intercept.

• In a table, the initial value is the input when the output is zero. In a graph, the initial value is the x-intercept.

• In a table, the initial value is the largest output value. In a graph, the initial value is the highest point on the curve.

• In a table, the initial value is the sum of all outputs. In a graph, the initial value is the area under the curve.

A teacher read part of a book to a class. The graph shows the number of pages read by the teacher over the next several days. What are the rate of change and the initial value?

• The rate of change is 10 pages per day and the initial value is 5 pages.

• The rate of change is 5 pages per day and the initial value is 0 pages.

• The rate of change is 2 pages per day and the initial value is 10 pages.

• The rate of change is 8 pages per day and the initial value is 2 pages.

A water park charges a rental fee plus $1.50 per hour to rent inflatable rafts. The total cost to rent a raft for 6 hours is $15. Assume the relationship is linear. What is the rental fee?

• $6

• $5

• $4

• $3

A teacher already had a certain number of canned goods for the food drive. Each day of the food drive, the class plans to bring in 10 cans. The total number of canned goods for day 10 is 205. Assume the relationship is linear. What is the rate of change and the initial value?

• Rate of change: 10 cans per day, Initial value: 105 cans

• Rate of change: 20 cans per day, Initial value: 5 cans

• Rate of change: 10 cans per day, Initial value: 10 cans

• Rate of change: 5 cans per day, Initial value: 150 cans

The rate of change and the initial value are key features of a linear relationship. Identify the rate of change and the initial value from the given context.

• The rate of change is 3 and the initial value is 2.

• The rate of change is 2 and the initial value is 3.

• The rate of change is 1 and the initial value is 0.

• The rate of change is 0 and the initial value is 1.

The rate of change and the initial value are key features of a linear function. Identify the rate of change and the initial value from the given context.

• The rate of change is 3 and the initial value is 2.

• The rate of change is 2 and the initial value is 3.

• The rate of change is 1 and the initial value is 0.

• The rate of change is 0 and the initial value is 1.

Multiple Representations: The Coughlin family is driving from Boston to Chicago. The total distance of the trip is 986 miles and each hour they will drive 65 miles. a. Algebra: Write an equation to represent the number of remaining miles y after driving any number of hours x.

• y = 986 - 65x

• y = 65x - 986

• y = 986 + 65x

• y = 65x