Problema Solution
Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480. Write an equation in the standard
form to represent the total rent (y) that Sam has to pay for renting the boat for x days. Part B: Write the equation obtained in Part A using function notation. Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
Answer provided by our tutors
Part A:
The Standard Form equation of a line has the following formula:
Ax+By=C, where A, B, and C are integers, and A is non-negative.
We will assume that when renting a boat Sam paid fixed cost and rental charge per day.
y = the total rent
x = the number of days
Sam rented a boat at $225 for 2 days would mean:
y = 225 when x = 2 or if we plug into Ax+By=C:
2A + 225B = C since A is non-negative we divide both sides by A
2 + (B/A)225 = C/A
He rents the same boat for 5 days, he has to pay a total rent of $480 means:
y = 480 when x = 5 days
5A + 480B = C since A is non-negative we divide both sides by A
5 + (B/A)480 = C/A
Now we have:
2 + (B/A)225 = C/A
5 + (B/A)480 = C/A
Lets denote s = B/A and t = C/A. Now we can write the following system of equations:
2 + 225s = t
5 + 480s = t
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click here to see the system of equations solved for s and t
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s = -1/85
t = -11/17 = -55/85
Now we can go back to:
B/A = -1/85 and C/A = -55/85
A = 85, B = -1, C = -55
The standard equation is:
85x - y = -55
Part B:
Using the equation 85x - y = -55 we solve for y
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click here to see the equation solved for y
........
y = 85x + 55
or in function notion y = f(x)
f(x) = 85x + 55
Part C:
The graph of y = 85x + 55 is:
