Answers:
Yes the data can be modeled with a linear equation.
Processing fee = 42 dollars; Daily fee = 102 dollars
Max number of days you can rent house = 11 days
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Explanation:
Part 1
Let
x = number of days
y = total cost in dollars
Note how each time x goes up by 2, y goes up by 204 (since 450-246 = 204). This consistent pattern directly tells us we have a linear equation going on. The next section goes into more detail.
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Part 2
The daily fee is directly tied to the pattern mentioned earlier. We have the cost going up by $204 each time 2 days go by. So the daily fee is 204/2 = 102 dollars per day.
You could also use the slope formula with say the first two columns of the table
m = (y2-y1)/(x2-x1)
m = (450-246)/(4-2)
m = 204/2
m = 102
This confirms the daily fee is $102.
You can use any two columns of the table that you want to get the slope. It doesn't have to be the first two columns.
Now use (x,y) = (2,246) along with m = 102 to find the y intercept. Like before you can use any column you want to form the (x,y) value.
y = mx+b
246 = 102*2+b
246 = 204+b
246-204 = b
42 = b
b = 42
The equation is y = 102x+42. The initial processing fee is $42. If you stayed at the house for x = 0 days, you still have to pay the fee y = 42.
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Part 3.
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 = 11.3529411764706
x = 11
We round down to the nearest whole number. This way we clear the hurdle.
Note that if x = 11, then,
y = 102x+42
y = 102*11+42
y = 1164
which is under the $1200 budget
In contrast, plugging in x = 12 leads to
y = 102x+42
y = 102*12+42
y = 1266
which is over the 1200 dollar budget. This shows that x = 11 is the max number of days you can rent the house.
