Answer: You have the correct answer. It is y = 150x-50
Nice work on getting the correct answer. For anyone curious, the explanation is below.
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x = number of hours the stand is open
y = amount earned
(1,100) is from the fact the stand is open 1 hour and earns $100
(3,400) is due to the stand earning $400 after 3 hours.
Slope Formula
m = (y2 - y1)/(x2 - x1)
m = (400-100)/(3-1)
m = 300/2
m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.
Use m = 150 and (x,y) = (1,100) to find the value of b as shown below
y = mx+b
100 = 150(1) + b
100 = 150 + b
100-150 = b
-50 = b
b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.
So we have m = 150 as the slope and b = -50 as the y intercept.
Therefore, y = mx+b turns into y = 150x-50.
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As a check, plugging in x = 1 should lead to y = 100
y = 150x-50
y = 150(1)-50
y = 150-50
y = 100 and indeed it does
The same should be the case with (3,400). Plug in x = 3 and we should get y = 400
y = 150x-50
y = 150(3)-50
y = 450-50
y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).
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