Question

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 1

@TheSmartOne

Answer 2

@jim_thompson5910

Answer 3

x = number of days
y = total cost

`Maria rented a coat at $285 for 3 days.`
one ordered pair is (3,285)

`she rents the same coat for 6 days, she has to pay a total rent of $510`
another ordered pair is (6,510)

Answer 4

find the equation of the line through (3,285) and (6,510)

Answer 5

510 - 285 / 6 - 3 ?

Answer 6

use parenthesis to properly group things up
(510-285)/(6-3)

Answer 7

but yes

Answer 8

that will give you the slope

Answer 9

Its asking for standard form, ax + by = c, how would I do that?

Answer 10

what slope did you get?

Answer 11

75

Answer 12

so pick any point, say (3,285) and use this point along with the slope to plug them into point-slope form

given point: (x1,y1) = (3,285)
x1 = 3
y1 = 285

slope: m = 75
\[\Large y - y_1 = m(x - x_1)\]
\[\Large y - 285 = 75(x - 3)\]
\[\Large y - 285 = 75x - 225\]
get this into the form Ax+By = C

Answer 13

How?

Answer 14

get the x and y terms to one side. Get everything else to the other side

Answer 15

So -60 = 75x - y?

Answer 16

or
75x - y = -60

Answer 17

it's in the form Ax+By = C where
A = 75
B = -1
C = -60

Answer 18

Ok, so that is the answer to a?

Answer 19

yes

Answer 20

I recommend you plug in each point, (3,285) and (6,510), to confirm that this is actually the line that goes through both points

Answer 21

I'll show you how to check (3,285)

x = 3
y = 285


75x - y = -60
75*3 - y = -60 ... plug in x = 3
75*3 - 285 = -60 ... plug in y = 285
225 - 285 = -60
-60 = -60 ... works

Answer 22

I could also use Desmos correct?

Answer 23

yes

Answer 24

It's always a good idea to practice plugging in the points just in case you're not able to use a graphing device on an exam

Answer 25

Vary steep XD.

Answer 26

jim its an online course so I should be fine, but if not I will check. Thanks! How do I do B?

Answer 27

you'll have to adjust the window

Answer 28

Part B) solve `75x - y = -60` for y. Then replace y with f(x)

Answer 29

-75x from both sides. -y = -60 - 75x. Divide it all by -1.
y = 60 + 75x
f(x) = 60 + 75x

Answer 30

yes or f(x) = 75x+60

Answer 31

Oh ok, Ill start putting it into correct format.

Answer 32

Now C. Would It simply be (3, 285) and (6, 510)?

Answer 33

Plot those two points on the same coordinate axis. Then draw a straight line through the points. Make sure the line extends as far as you can in both directions.

Answer 34

I am not supposed to do that, it says describe how to.

Answer 35

I just described it

Answer 36

Oh ok I thought you were telling me to do that XD

Answer 37

You can if you want, but the two ideas are very similar

Answer 38

A: 75x - y = -60

B: f(x) = 75x + 60

C: Plot those two points on the same coordinate axis. Then draw a straight line through the points. Make sure the line extends as far as you can in both directions.

Answer 39

Look good?

Answer 40

be sure to elaborate on what you mean by "those two points" for part C

Answer 41

Plot those two points (3, 285) and (6, 510) on the same coordinate axis. Then draw a straight line through the points. Make sure the line extends as far as you can in both directions.

Answer 42

good

Answer 43

Thanks I gave you a medal and a fan and a testi