Constant Rate of Change

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation to find out how many hours, h, they rented the Boat if the total cost was $33.

• h = 2(9) + 15
• 33 = 15h + 2
• h = 15(9) + 2
• 33 = 2h + 15

Multiple Choice

The 30 members of a choir are trying to raise $1500 to cover travel costs to a signing camp. They have already raised $600. Which equation would you solve to find the average amount each member can raise in order to meet the goal?

• 30x + 600 = 1500
• 30x - 600 = 1500
• x + 600 = 1500
• 30x = 1500

Multiple Choice

-4x + 14 ≤ 54

• x ≥ - 10
• x ≤ -10
• x ≥ 10
• x ≤ 10

Constant Rate of Change

Part 1:

Unit Rate & Constant of Proportionality

​UNIT RATE...

​*How much of something per 1 unit of something else.

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​Examples:

• 100 cars pass by in 2 hours. The unit rate is 50 cars per hour.

• ​In the last 4 weeks Sam earned $2000. The unit rate is $500 per week.

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​

​Can you think of any more examples?

Multiple Choice

A store has 120 customers in 6 hours. What is the unit rate in customers per hour?

• 16 customers per hour

• 12 customers per hour

• 20 customers per hour

Multiple Choice

You're throwing a party, and you ordered 15 pizzas for your guests. Your total came to $97.50. What was your unit cost per pizza?

• $4.95 per pizza

• $5.75 per pizza

• $6.50 per pizza

​CONSTANT OF PROPORTIONALITY

​*The ratio between two directly proportional quantities. (Think about the "rule" of a table!)

​

How do we find it?

​

k= y/x

​CONSTANT OF PROPORTIONALITY

How can we do this from a word problem?

​

​A recipe says to use 3 cups of flour to make 48 cookies. What is the constant of proportionality that relates the number of cookies made, y, to the number of flour used, x ?

​

​

​k= y/x

​CONSTANT OF PROPORTIONALITY

How can we do this from a table?

​

​

​We can use any of the corresponding

x and y-values!

​

​k= y/x

​

​CONSTANT OF PROPORTIONALITY

What about from a graph?

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​We need to find an x and y value!

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Find a point and let's use the ordered pair!

​

​

​​k= y/x

Multiple Choice

What is the constant of proportionality for this table?

• 1/9
• 9
• 8

Multiple Choice

Justin ordered 5 ice cream bars for $12.25. What is the constant of proportionality that relates y, the total cost of x ice cream bars?

• $2.45
• $4.00
• $7.25
• $1.25

Multiple Choice

What is the constant of proportionality? 

• 45 mph
• 90 mph
• 135 mph
• 2 mph

Multiple Choice

What is the constant of proportionality? 

• 4
• 1/4
• 8
• 1/8