A manufacturer of bicycles has determined that 550 bikes per month will be sold at a price of $250. At a price of $150, it is estimated that 750 bikes will be sold.

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a) Determine a linear function (equation) that predicts the number of bikes that will be sold each month at any given price.

b) Use your equation from question a to predict how many bikes will be sold at $350.

550 bikes are sold at a price of $250, this can be represented by (550, 250). Also, 750 bikes is sold at a price of $150, hence it is represented by (750, 150)

A linear function is represented by:

y = mx + b

m is the slope, b is the y intercept.

Therefore the function is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-250=\frac{150-250}{750-550} (x-550)\\\\y=\frac{1}{2}x-25[/tex]

The number of bikes sold for $350 is:

350 = (1/2)x - 25

x = 750

Therefore 750 bikes would be sold for $350

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