Part A
Select any two columns from the table to compute the slope
I'll pick the first two columns to select (2,246) and (4,450)
m = (y2-y1)/(x2-x1)
m = (450-246)/(4-2)
m = 102
The slope is 102. This is the daily fee. It is the cost per day to rent the beach house. This does not include the processing fee, which is the y intercept. We'll use this m value along with one of the columns of the table to help find the value of b.
y = mx+b
246 = 102*2+b
246 = 204+b
246-204 = b
42 = b
b = 42
The processing fee is $42, which is the initial starting amount of money you must pay to get the beach house (even if it turns out you never use it for a single day). Then you'll pay $102 per day on top of that $42.
Because m = 102 and b = 42 are the slope and y intercept, we go from y = mx+b to y = 102x+42
The variable x stands for the number of days. The variable y is the total cost in dollars.
Answer: y = 102x+42
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Part B
Refer to part A for the steps and explanation.
Processing fee = $42
Daily fee = $102
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Part C
The budget is $1200. This means the total cost y cannot be larger than 1200.
Plug in y = 1200 and solve for x.
y = 102x+42
1200 = 102x+42
1200-42 = 102x
1158 = 102x
102x = 1158
x = 1158/102
x = 11.35294 which is approximate
Round down to the nearest whole number to get x = 11.
If x = 11, then,
y = 102x+42
y = 102*11+42
y = 1164
which is under the $1200 budget. However, if x = 12, then
y = 102x+42
y = 102*12+42
y = 1266
which is now over budget. Therefore, the highest x can get is x = 11.
Answer: 11 days