Question

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)

Answer 1

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

---------------

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.

Answer 2

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

Let

x-------> the number of days

y------> the total rent

A------> point (2,225)

B------> point (5,480)

Step 1

Find the slope AB

`m=((y2-y1))/((x2-x1))`

`mAB=((480-225))/((5-2))`

`mAB=((255))/((3))`

`mAB=85`

Step 2

with m=
`85` and the point A Find the equation of the line

`y-y1=m*(x-x1)`

`y-225=85*(x-2)`

`y=85x-170+225`

`y=85x+55`

we know that

the equation of the line in the standard form is equal to

`Ax+By=C`

so

`-85x+y=55`

therefore

the answer part 1) is

`-85x+y=55`

Part 2)Write the equation obtained in Part A using function notation

`f(x)=85x+55`

the answer Part 2) is

`f(x)=85x+55`

Part 3)Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Graph the equation by striking a line through the points
`(2,225)` and
`(5,480)`

using a graph tool

see the attached figure