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. (4 points) part b: write the equation obtained in part a using function notation.(2 points) part c: describe the steps to graph the equation obtained above on the coordinate axes. mention the labels on the axes and the intervals. (4 points)

PART A:

y = mx + C

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When x=2, y=225.

When x=5, y=480.

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Therefore:

2m + C = 225

5m + C = 480

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5*(2m+C)=5*225

2*(5m+C)=2*480

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Therefore:

10m + 5C = 1125

10m + 2C = 960

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Therefore:

10m = 1125 - 5C

10m = 960 - 2C

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Therefore:

960 - 2C = 1125 - 5C

3C = 165

C = 55

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y=mx + 55

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2m + C = 225

Therefore:

2m + 55 = 225

2m = 225 - 55

2m = 170

m = 85

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PART B:

Which means that:

y=85x + 55

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PART C & D:

Graph the equation by striking a line through the points (2,225) and (5, 480), but remember that x cannot be equal to 0, so this line shouldn't go through the point (0,0) or points whereby x is less than the value 0.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for