Direct Variation and Linear Models

The value of y varies directly with x, and the constant of variation is 6. What is the value of x when y = 54?

• 6

• 9

• 54

• 324

The table represents a direct variation. Write the direct variation equation for the data.

Dan bought 3 bags of potting soil and spent $3.75. Does this situation represent a direct variation?

• yes

• no

Dan bought 3 bags of potting soil and spent $3.75. How much would Dan spend for 7 bags of potting soil?

Which linear equation does not represent a direct variation?

• y=5x

• y=-8x

• y=-6x-9

• y= x/8

Which linear graph does not represent a direct variation?

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Erin is starting a yard care business. A lawn mower and other supplies will cost her $450. She plans to charge $15 for each hour that she works. Write a function p(x) for the profit Erin will earn for working x hours. (Hint: Profit is equal to earnings minus expenses.)

• p(x) = 450 - 15x

• p(x) = 450 + 15x

• p(x) = 15x - 450

• p(x) = 15x + 450

Erin is starting a yard care business. A lawn mower and other supplies will cost her $450. She plans to charge $15 for each hour that she works. Erin estimates that an average job will take about 1.5 hours. How many jobs must Erin have to break even? Explain your answer. (Hint: Erin will break even when her profits are equal to 0.)

A school is holding a craft fair as a fundraiser. An artist donates $25 to rent a table at the fair. In addition, each artist must donate $2 for each item sold to the school’s art program. The table shows the total amount that an artist will donate if he or she sells 0, 1, 2, and 3 items. Write a function f(x) for the total amount an artist donates for selling x items.

If an artist sells 45 items, how much will he or she donate?

• $90

• $115

• $205

• $465