Interpreting Rate of Change and Initial Value

Interpreting Rate of Change and Initial Value

Bonnie has decided to join a gym for the next 3 months.

Fabulous Fitness charges $45 per month.

Greg’s Gym charges $99 every 3 months.

How can she compare the two options to determine the better value?​

​Bonnie continues to research gym options and finds out that Fabulous Fitness has no sign-up fee, while Greg’s Gym charges $50 for the initial sign-up.

She makes the following table to help her compare the two options.

​Take a minute to examine the information before answering the next few questions.

Fill in the Blank

According to the graphic, Bonnie would need to pay $__ to join Fabulous Fitness.

Fill in the Blank

Bonnie would need to pay $__ to join Greg's Gym.

The initial value of any function represents the value of the function at the beginning.

Initial Value

Fabulous has an initial value of 0 because they do not charge a sign-up fee.

Greg's Gym has an initial value of 50 because they charge a sign- up fee of $50.

Fill in the Blank

How much does it cost per month at Fabulous Fitness?

(Type your answer in digits, not words)

Fill in the Blank

How much does it cost per month at Greg's Gym?

(Type your answer in digits, not words)

The rate of change of any function represents the constant value at which the function increases or decreases.

Rate of Change

Fabulous has a rate of change of 45 because they charge $45 per month

Greg's Gym has a a rate of change of 33 because when split evenly between 3 months, it costs $33 per month.

Multiple Choice

If the data for each gym was graphed on a coordinate plane, which gym would have a point on the origin (0,0)?

• Fabulous Fitness

• Greg's Gym

Open Ended

Why would Fabulous Fitness have a point that passes through the origin? Explain your reasoning using the information in the image.

Multiple Choice

The owner of Fabulous Fitness wants to buy name tags for her staff.

She writes the following function to represent the cost, y, for a certain number of name tags, x.

y = $2.00x + $7.00

What is the rate of change (CROC)?

• $2.00 per tag

• $7.00 per tag

Multiple Choice

The owner of Fabulous Fitness wants to buy name tags for her staff.

She writes the following function to represent the cost, y, for a certain number of name tags, x, from an online vendor.

y = $2.00x + $7.00

What is the initial (starting) value?

• $2.00

• $7.00

Open Ended

Given that $7.00 is the initial value, what could that initial cost represent in the total cost for purchasing the name tags?

​Cost of Name Tags

The function representing the cost of the name tags purchased is shown in the graph.​

Examine the graph before answering the next few questions.

Fill in the Blank

If x represents the number of name tags purchased. Complete the ordered pair below by determining in the missing coordinate of the point on the graph.

(10, ___)

**Remember it costs $2 per tag plus the $7 initial fee.

Open Ended

Complete the statement below:

The point (10, 27) means that it will cost $_____ for ______ name tags.

As a reminder, when an equation is written slope-intercept form, the "m" represents the slope/CROC

Now we know that the "b" represents the y-intercept or the "initial value" of the function.

Slope-Intercept Form

OR

INITIAL VALUE!

Multiple Choice

The graph represents the money in a savings account.  What is the meaning of the y-intercept?

• The initial deposit was $30

• $30 is added to the account each week

• It took 30 weeks to same enough money to open an account

• not enough information

Multiple Choice

The graph represents the height of a burning candle.  What is the meaning of the y-intercept?

• the time it takes to burn the entire candle

• the rate at which the candle is losing height

• the change in the height of the candle each hour

• the original height of the candle

Multiple Choice

Which statement matches the graph?

• Taylor can write 6 words per minute

• Taylor can write 25 words per minute

• Taylor can write 50 words per minute

• Taylor can write 150 words per minute

Multiple Choice

Janice is saving money for retirement. The equation y = 500x + 12,000 models her retirement savings where y is the total she has saved in dollars, and x is the number of months.

Interpret the y-intercept.

• Janice started with $500 in her account

• Janice started with $12,000 in her account

• Each month, Janice saves an additional $500

• Each month, Janice saves an additional $12,000

Multiple Choice

An air conditioning salesman earns a base salary plus a commission for each air conditioner her sells.

The equation y = 375 + 125x represents his pay based on the number of air conditioners he sells each week.

What is the slope and what does it represent?

• The slope is 375 and represents the amount he earns for each air conditioner.

• The slope is 125 and represents the amount he earns for each air conditioner.

• The slope is 375 and represents the base salary.

• The slope is 125 and represents the base salary.