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

So we'll write it in point-slope form first, then convert it into standard form.

Answer 2

ok so...

Answer 3

So find out the slope first

Answer 4

The slope of a function is rise over run, or y-distance/x-distance, or in this context "the increase of rent over the increase of number of days"

Answer 5

255 over 2

Answer 6

or 127.5 over 1?

Answer 7

Please be noted that I'm talking about "the increase" instead of the actual amount

Answer 8

From $225 for 2 days to $480 for 5 days

Answer 9

What's the increase of rent over the increase of number of days?

Answer 10

255 over 3

Answer 11

or 85 per day?

Answer 12

Yep

Answer 13

So the answer for a is 85

Answer 14

Nope, 85 is just the slope of function

Answer 15

so umm
=85x+y

Answer 16

Nope, the equation given by a function with known slope \(m\) and a known point \(x_1,y_1\) is given by:
\[y-y_1=m(x-x_1)\]

Answer 17

so umm y - y = 85(x - x)
i cant write the small 1

Answer 18

No, \(x_1,y_1\) is a point on the function

Answer 19

You can use (2,225) or (5,480)

Answer 20

225 - 480 = 85(2 - 5)

Answer 21

The \(x\) and \(y\) are not to be substituted

Answer 22

ohh so y = 225 = 85(x - 2)

Answer 23

exactly

Answer 24

Now convert it into standard form

Answer 25

what was it?

Answer 26

Just expand everything and put everything on the left hand side of the equation

Answer 27

how do you expand

Answer 28

I mean distribute

Answer 29

how?

Answer 30

like umm 225 = 85x - 2

Answer 31

y - 225 = 85(x - 2)
y - 225 = 85x - 170
y = 85x - 170 + 225
y = 85x + 55
0 = 85x - y + 55
85x - y + 55 = 0

Answer 32

i might have done this ine thing inccorectly
25 = 85x + 2

Answer 33

YOOHOO?

Answer 34

and btw we got this, and 2 more and they have to be done by 12:30

Answer 35

If you don't get the concept, useless for us to give you the answer

Answer 36

Still, please help me

Answer 37

85x - y + 55 = 0

Answer 38

you sure?

Answer 39

i dont understand the 0 at the end

Answer 40

hello @kc_kennylau

Answer 41

Which step in
y - 225 = 85(x - 2)
y - 225 = 85x - 170
y = 85x - 170 + 225
y = 85x + 55
0 = 85x - y + 55
85x - y + 55 = 0
did you not understand?

Answer 42

I can explain step by step

Answer 43

no i just dont understand why 0 at the end!

Answer 44

so the total cost is just 0

Answer 45

Nah, the rent is y

Answer 46

oh ok

Answer 47

Ok lets do b now

Answer 48

85x - y + 55 = 0
85x + 55 = y
y = 85x + 55
f(x) = 85x + 55

Answer 49

For part C, I don't know how you'd describe it, but basically the concept is you plot the two points (2,225) and (5,480) out and then join them

Answer 50

I'll leave the detail to you

Answer 51

ok thanks are you ready for 2 more?

Answer 52

No I have to go now

Answer 53

ok then bye