Compare Rates of Change for Functions

Randy charges his tenants $400 each month to rent his houses plus $600 security deposit. In the new year, the property taxes increased on the area where he rents so as a result he must increase the rate of change by $25 to ensure his profits are not harmed. Write an equation that best represents how much his tenants will now have to pay.(*Remember rate of change is the slope.)

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The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. Find the equation for Beth's service. Which service is cheaper for 8 movies in one month?

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Who is losing weight faster?

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Charlie rented a moving truck. He paid a daily fee plus a per-mile fee to rent the truck. The equation below represents the daily amount Charlie paid for the truck if he drives it x miles.

y = 1/2x + 10

What does the slope (m) of the graph of this equation represent?

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Equation A: y = 2x + 3

Equation B: y = 3x - 3

Which equation has a higher slope?

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Rich is a member of a gym. He pays a monthly fee plus a per-visit fee. The equation below represents the monthly amount Rich pays for his membership to the gym per month for x visits. y = 3x + 10 What does the y-intercept (b) of the graph of this equation represent?

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What is the rate of change (slope) to rent a raft from Water's Edge Rafts?

• $6 per hour

• $5 per hour

• $1 for 6 hours

• $1 for 5 hours

Which company shows a greater rate of change?

• Water's Edge Rafts

• Ryan's Rafts

Randy charges his tenants $400 each month to rent his houses plus $600 security deposit. In the new year, the property taxes increased on the area where he rents so as a result he must increase the rate of change by $25 to ensure his profits are not harmed. What equation best represents how much his tenants will now have to pay?

• y = 425x + 600

• y = 425 + 600x

• y = 400x + 625

• y = 400 + 625x

What is the rate of change (slope) to rent a raft from Ryan's Rafts?

• $15 per hour

• $2.25 per hour

• $17.25 per hour

• $1 per hour