Question

Who’s right? And why?

Answer 1

Answer: Raymond is correct

The DJ charges $75 an hour.

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Step-by-step explanation:

x = number of hours

y = total cost

The DJ does a 3-hour event for $275. This means one point is (x,y) = (3,275)

Another point is (5,425) because a 5-hour event costs $425.

Let's find the slope of the line through these two points.

`(x_1,y_1) = (3,275) \text{ and } (x_2,y_2) = (5,425)\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\m = (425 - 275)/(5 - 3)\\\\m = (150)/(2)\\\\m = 75\\\\`

The slope is 75, meaning that each time y goes up by 75, x goes up by 1.

Flipped around it means each time x goes up by 1, y goes up by 75.

This means each time we add on an extra hour, the cost goes up by $75.

The DJ charges $75 an hour. Raymond is correct.