Question

Jill owns a cupcake shop. In her 2nd month of business, Jill sold 330 cupcakes. In the 6th month, she sold 918 cupcakes. The growth of the business can be modeled by a linear equation.

Answer 1

The linear expression which models Jill's business growth is y = 147x + 36

Sales made by Jill :

• 2nd month = 330 cupcakes
• 6th month = 918 cupcakes

General form of a linear model :

• y = bx + c
• y = final or predicted amount
• b = slope or growth rate
• c = intercept
• x = number of months

We can calculate the amount sold per month :

• (6th month sale - 2nd month sale) / Number of months

• b = (918 - 330) / (6 - 2) = 588 / 4 = 147

Using the second month ;

330 = 147x + c

x = 2

330 = 147(2) + c

330 = 294 + c

c = 330 - 294

c = 36

Therefore, the linear model can be expressed thus ;

• y = 147x + 36

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