Question

ALGEBRA 1. MEDAL GIVEN. PLEASE HELP.
Part A: Nadia rented a stage platform at $410 for 4 days. If she rents the same stage platform for 8 days, she has to pay a total rent of $770.

Write an equation in the standard form to represent the total rent (y) that Nadia has to pay for renting the stage platform 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

for Part A, i got y = (410 / 4)x
is that correct???

Answer 2

@Nnesha

Answer 3

i really only need help with part c.

Answer 4

b*

Answer 5

A looks good :)
Having trouble with the function notation?

Answer 6

thank you. :)
yes!

Answer 7

Oh oh maybe we screwed something up...
Notice the second piece of information about the 8 days?
Hold on hold on hold on >.< gimme a sec

Answer 8

oh alright. take your time. :)

Answer 9

Since this is Algebra 1, I'm assuming that we're looking for a linear model.
So we want something of the form: \(\Large\rm y=mx+b\)

Answer 10

We need an equation that will satisfy BOTH pieces of information, not just the first piece.

Answer 11

Let's take that information and think of it as ordered pairs:\[\Large\rm (4,410)\]\[\Large\rm (8,770)\]

Answer 12

Understand what I did there? :o

Answer 13

ummm yes. i believe so.

Answer 14

The 4 relates to the $410. That's our first set of data.
Same with the other stuff.

We want to use our slope formula, to figure out the slope of our linear function.

Answer 15

right

Answer 16

\[\Large\rm m=\frac{y_2-y_1}{x_2-x_1}\]This look familiar? :o

Answer 17

yes!

Answer 18

Plug in the stuff :D Get a number. Give it a try!

Answer 19

wait, what is y2, y1, x2, x1?? how do i find those??

Answer 20

Time is independent. Those are what we call our x's.
So the number of days are the x's.

Answer 21

So when I set up my ordered pairs, that's why I put the 4 and 8 in the first slots.
Those are what we want to call our x's.

Answer 22

ohhhhh.

Answer 23

then the y's would be the cost???

Answer 24

Yes :)
The cost DEPENDS on the amount of days past.
That's just something to keep in mind:
x - independent
y - dependent
kinda hard to stuff everything in your brain noggin though :d I know

Answer 25

so it would be:
m = 770 - 410 / 8 - 4
???

Answer 26

Mmmm ok the setup looks good!
Finish up the calculations to get a single number for your m :)

Answer 27

m = 90 ???

Answer 28

\[\Large\rm y=mx+b\]\[\Large\rm y=90x+b\]Ok great! Almost done figuring out our equation.

Answer 29

So this equation is telling us that it costs 90 dollars PER day to rent the stage.
But there might also be some type of "service charge" or something going on.
It's a value that doesn't change, it's just always charged to you no matter how many days you rent the stage.

Answer 30

We'll plug in one of our points to solve for the unknown b.\[\Large\rm (4,410)\qquad\to\qquad ~\quad y=mx+b\]\[\Large\rm (4,410)\qquad\to\qquad 410=90(4)+b\]

Answer 31

wait, if this equation says it costs 90 dollars per day, my first equation in part A is wrong.

Answer 32

Yes, we're fixing part A :o

Answer 33

ohhhhh okay.

Answer 34

Understand how I plugged that information in?
I put the 4 in for the x, the 410 in for the y,
then you want to solve for b.

\[\Large\rm 410=90(4)+b\]\[\Large\rm 410=360+b\]Understand how to solve for b from this point?

Answer 35

subtract 360 from 410????

Answer 36

mmm k good.

Answer 37

\[\Large\rm 410-360=b\]\[\Large\rm 50=b\]We'll take our b value that we found,
and plug it back into our equation.
(The one that doesn't have the 4 and 410 plugged in).\[\Large\rm y=90x+b\]\[\Large\rm y=90x+50\]

Answer 38

Mmmm k so there's part A, yah? :)
A lil harder than you were expecting maybe? Hehe

Answer 39

so part a:
y = 90x + 50

Answer 40

yes.

Answer 41

okay thank you! haha.
could you also help me with part b????

Answer 42

Part B is nice and easy.
Instead of y, we're going to clearly show that the Rent has a dependency on time by writing it as a function of our time variable x.

Answer 43

So we simply replace y with f(x).

Answer 44

For part B:
\[\Large\rm f(x)=90x+50\]

Answer 45

And how bout C?
You think you can handle the graphing? :)

Answer 46

thank you so much!
and i think...but just in case, could we go over it really quick? :)

Answer 47

\[\Large\rm y=4x+3\]I'll show you an example :3
and make you do yours on your own hehe

Answer 48

haha okay.