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.