Comparing Rate

Sal mows lawns. He charges $40 per hour he spends mowing, he also charges a fee of $10 for weed-eating.

Which equation models Sal's business plan?

• y = 10x + 40

• y = 40x + 10

• y = 40x + 50

• y = 10x - 40

Answer explanation

$40 per hour indicates that the rate of change is 40.

In our equations, our rate of change is next to our variable (x).

Sal will only weed-eat one time per lawn, so that is an initial value that only happens one time.

y = 40x + 10

Sal mows lawns. He charges $40 per hour he spends mowing, he also charges a fee of $10 for weed-eating.

Which table models Sal's business plan?

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Answer explanation

Our equation is y = 40x + 10

Which means we start at 10. Essentially meaning that when our x value is 0, our y value must equal 10.

From there we go up by 40 each time our x value goes up by one. This is a rate of change of 40.

Sal mows lawns. He charges $40 per hour he spends mowing, he also charges a fee of $10 for weed-eating.

Which graph models Sal's business plan?

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Answer explanation

Our equation is y = 40x + 10

Which means our y intercept is 10, and our slope is 40 over 1

Abe has a $20 iTunes gift card. Every day, Abe buys a $3 song.

Pick the equation below that models the amount of money left on the gift card over time.

• y = 20x + 3

• y = 3x + 20

• y = -3x + 20

• y = 20x - 3

Answer explanation

Abe starts with $20 making it the initial value.

The rate of change is 3, however, because the amount of money on the card is going down, it is considered a negative. Making the rate -3.

Our equation is y = -3x + 20

Abe has a $20 iTunes gift card. Every day, Abe buys a $3 song.

Pick the table below that models the amount of money left on the gift card over time.

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Answer explanation

Abe starts with $20 making it the initial value. (0,20) is the first set in our table.

He spends $3 a day, meaning the value of his table is going down each time by 3.

Abe has a $20 iTunes gift card. Every day, Abe buys a $3 song.

Pick the table below that models the amount of money left on the gift card over time.

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Answer explanation

With the equation y = -3x + 20, our initial value is 20, and our slope is -3/1.

The county fair charges $5 for parking. They also charge $5 for every 3 carnival rides.

Pick the equation below that models the amount of money somebody would spend at the fair.

• y = 5x + 3

• y = 3x + 5

• y = 3/5x + 5

• y = 5/3x + 5

Answer explanation

Parking is a one-time fee, so the initial value is $5.

The slope is more challenging. For every 3 rides, it costs $5.

Since rides are the independent variable, it means that our change in x is 3. Leaving our change in y to be 5. Giving us a slope of 5/3 (dollars per ride)

The county fair charges $5 for parking. They also charge $5 for every 3 carnival rides.

Pick the table below that models the amount of money somebody would pay to go to the fair.

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Answer explanation

The 5 dollars for parking is the initial value, meaning when x = 0, y = 5.

The change in x (rides) is 3, so the x values need to change by 3 each time.

The change in y (dollars) is 5, so the y values need to change by 5 each time.

The county fair charges $5 for parking. They also charge $5 for every 3 carnival rides.

Pick the graph below that models the amount of money somebody would pay to go to the fair.

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Answer explanation

Our equation is y = 5/3x + 5

Our y-intercept is 5, and our slope is up 5 over 3.

Pick every description below that fits the equation

y = 4x + 10

• Gerardo is 10 miles from school when he begins his afternoon jog. He is jogging 4 miles per hour.

• Abigail knocks down 4 pins every time she bowls. On the last frame, she bowls a strike. (A strike is 10 pins.)

• Bryan pays $10 a month for his music streaming app. In July he donates $4 to a charity drive run through the app.

• Loren is making homemade chili. Her recipe calls for 10 ounces of ground beef and 4 ounces of beans for every person who is going to eat the chili.

• Ashley loves Girl Scout cookies and has already eaten 10 Thin Mints. Every hour she cant help but eat 4 more Thin Mints.

Answer explanation

Gerardo starts at 10 and changes 4 per mile.

Abigale changes 4 per bowl, except for the one time when she hits 10.

Bryan starts at 10 and changes by 4 each time.

Loren is changing the number of ounces by 14 each time. (and I'm not even sure if I want to count beef and beans as the same variable.)

Ashley has started with 10 and changes by 4 each time.