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)=5225

2(5m+C)=2480

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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.

calculista calculista · Answer 2 · 2018-08-01T22:33:09-04:00

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

$m=\frac{(y2-y1)}{(x2-x1)}$

$mAB=\frac{(480-225)}{(5-2)}$

$mAB=\frac{(255)}{(3)}$

$mAB=85$

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