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See the image below, thank you so much!!

See the image below, thank you so much!!-example-1

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3 votes

Answers:

y + 1 = 3(x - 1)

x ≥ 2

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Explanation for part A

The line goes uphill when moving to the right. Therefore the slope is positive. This eliminates choices C and D since those have negative slopes.

The slope must be m = 3 based on what choices A and B state.

The graph goes through (x1,y1) = (1,-1)

Plug those three items into the point slope form

y - y1 = m(x - x1)

y - (-1) = 3(x - 1)

y + 1 = 3(x - 1)

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Explanation for part B

Let's solve the previous equation for y.

y + 1 = 3(x - 1)

y + 1 = 3x - 3

y = 3x-3-1

y = 3x-4

This has slope 3 and y intercept -4.

The company profits when y > 0, i.e. when the total bill for the customer is some positive number.

y > 0

3x-4 > 0

3x > 4

x > 4/3

x > 1.333 approximately

Rounding up to the nearest whole number has us arrive at x ≥ 2 which is a reasonable domain so the company profits.

Notice if x = 1, then the company pulls in y = -1 dollars, i.e. they lose $1

But if x = 2, then the company makes y = 2 dollars.

If x = 3, then the company makes y = 5 dollars.

And so on.

Each time x goes up by 1, y goes up by 3, which is the slope value.

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