Question

math help asap?

Answer 1

Part A: Maria rented a coat at $285 for 3 days. If she rents the same coat for 6 days, she has to pay a total rent of $510.

Write an equation in the standard form to represent the total rent (y) that Maria has to pay for renting the coat 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 2

@mathmale

Answer 3

First, you could graph the two given points (3, $285) and (6, $510). If you do, and if you then draw a straight line thru the two points, you'll see that this line crosses the y-axis once. Where? That point is called your "vertical incercept."

This experiment will show you that your function is a linear one; it has a (constant) slope and a vertical intercept. How would you go about determining what the slope of this line is?

Answer 4

Or, without graphing

\(\normalsize\color{blue}{ 3x+b=285 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 6x+b=510 \LARGE\color{white}{ \rm │ }}\)

Answer 5

If you prefer graphing, I advise, https://www.desmos.com/calculator .

Answer 6

Would slope = 75? @mathmale

Answer 7

I doubt that...

\(\normalsize\color{blue}{3x+b=285 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 6x+b=510 \LARGE\color{white}{ \rm │ }}\)
───────────────
\(\normalsize\color{blue}{6x+2b=570 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 6x+b=510 \LARGE\color{white}{ \rm │ }}\)
───────────────
\(\normalsize\color{blue}{b=60 \LARGE\color{white}{ \rm │ }}\)
───────────────
\(\normalsize\color{blue}{3x+60=285 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 6x+60=510 \LARGE\color{white}{ \rm │ }}\)
───────────────
\(\normalsize\color{blue}{3x=225 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 6x=450 \LARGE\color{white}{ \rm │ }}\)
───────────────
\(\normalsize\color{blue}{x=75 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ x=75 \LARGE\color{white}{ \rm │ }}\)

YES !!!!

Answer 8

I first wrote I doubt that,. sorry

Answer 9

You are right.

Answer 10

Dang, I messed it all up !!

Answer 11

You have two points (as explained above). Use the slope formula to determine the slope of the line connecting these two points. This formula is \[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 12

would you please re-calculate the slope, using this formula. Show all your work, please.

Answer 13

yeah, that would be easier, slope formula, how would I ever forget about it (?!)

Answer 14

75 = 510 - 285
------------
6 - 2

Would this be right starting it off? @mathmale

Answer 15

not 2 , 3

Answer 16

My bad typo!

Answer 17

510 - 285
------------ is fine. How'd you get that 75? check your math, please.
6 - 2

Answer 18

(510-285)/(6-3) = 225/3 = 75

Answer 19

Again: Your goal here is to find the SLOPE of the straight line connecting the points (3,$285) and (6,$510).
I do not get 75. Check your math once more, please.
First find 510-285.
Next, find 6-3.
Last, divide the 2nd result into the first.

Answer 20

yes, you got the slope, and in my solution for slope I (accidentally) solved for the y-intercept first.

Answer 21

Alright so
510-285 = 225
6 - 3 = 3
What do I do with the 225?

Answer 22

So, y=mx+b plug in your `m ` and ` b `

Answer 23

CoolCat: Stop for a moment. Definie your current goal. What are you trying to find?

Answer 24

the Slope

Answer 25

Yes, and that 225 is the INCREASE in y; that 3 is the increase in x; knowing these two facts, how do you find the slope of the line thru the 2 points?

Answer 26

This is the slope formula:\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 27

The change in y is 225; the change in x is 3. What is the slope?

Answer 28

I just got lost again :/ Agh.

Answer 29

Earlier, you asked me whether this was OK:

75 = 510 - 285
------------
6 - 2

and I said yes. But now I've seen that you have 6-2 in the denominator; you should have 6-3.

Answer 30

Yeah that was a typo sorry

Answer 31

Let's wrap this up:

the change in y as x increases from 3 to 6 is $225.
The change in x is 6-3 = 3 days.

The slope is (change in y) / (change in x).

Do this computation, please.

Answer 32

Ohhh I see now so
(225,3) ?

Answer 33

that is how you'll compute the slope. What is the slope?

Answer 34

Divide 3 into 225, please.

Answer 35

0.0133...

Answer 36

no. if you're using a calculator, type in 225 first, then the DIVIDE key, and then 3.

Answer 37

75..

Answer 38

Yes. That's your slope.
Now, choose EITHER (but not both) of the points (3,$285) and (6,$510).

Insert the appropriate coordinates of this point into the point-slope formula for the equatin of a straight line:

Answer 39

\[y-y _{1}=m(x-x _{1})\]

Answer 40

does it matter which spot I put them in as long is its in the x or y spot?

Answer 41

The order of the x- and y-coordinates of each point IS important.

Answer 42

If y ou choose the point (3,$285), x=3 and y=$285.

Answer 43

y - 285 = m (x - 3)

Answer 44

Very nice, and what is the value of the slope, m?

Answer 45

am I using the slope we just found?

Answer 46

yes

Answer 47

coolcatsclan: You were right all along:

"coolcatsclan
Would slope = 75?"

Finish writing out that equation, please. Substitute 75 for m.

Answer 48

y - 285 = 75 (x- 3)

Answer 49

Very nice. You could either leave this equation as-is, or you could solve it for y.
To solve it for y, add 285 to both sides. Do that now, please.

Answer 50

y - 285 = 75 ( x - 3)
+285 +285
y = 75x + 60 ?

Answer 51

Beautiful. You're done. Questions?

Answer 52

parts b and c ?

Answer 53

By solving that previous equation for y, you have answered Part B already. You could alternatively write it as y=f(x)=y = 75x + 60

Answer 54

which is in "functional notation."

Answer 55

What would I do for c? @mathmale

Answer 56

I'm sure you've graphed straight lines before. Think back to that experience and then do your best to answer Part C. I need to see your efforts first; then I'll give you feedback.

Answer 57

Thank you for your help. @mathmale

Answer 58

My pleasure!