Question

There is a new food delivery company that charges $10 to deliver 3 meals and $16 to deliver
12 meals. If the charging rate remains constant, how much will it cost to deliver 9 meals?

Answer 1

Using a linear function, it is found that it will cost $14 to deliver 9 meals.

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A linear function has the following format:

$y = mx + b$

In which

• m is the slope(rate of change).
• b is the y-intercept(value of y when x = 0).

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• To build the linear function, we use the two points given by the exercise:  (3,10), (12,16)

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The slope is given by the change in y divided by the change in x, thus:

• Change in y: 16 - 10 = 6
• Change in x: 12 - 3 = 9
• Slope: $m = \frac{6}{9} = \frac{2}{3}$

Thus:

$y = \frac{2}{3}x + b$

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• Using one of the point, we can find b.
• I am going to use (3,10), which means that when $x = 3, y = 10$. Thus:

$y = \frac{2}{3}x + b$

$10 = \frac{2}{3}(3) + b$

$2 + b = 10$

$b = 8$

The cost of delivering x meals is given by:

$y = \frac{2}{3}x + 8$

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The cost of delivering 9 meals is y when x = 9, thus:

$y = \frac{2}{3}(9) + 8 = 2\times3 + 8 = 6 + 8 = 14$

It will cost $14 to deliver 9 meals.

A similar problem is given at https://brainly.com/question/21010520