Question

MEDAL & FAN


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

so just do what it says

Answer 2

First find the slope.

We have two points:

(3, 285) and (6, 510)

Plug them into the slope formula:

\(m = \dfrac{y_2-y_1}{x_2-x_1}\)

\(m = \dfrac{510-285}{6-3}\)

Answer 3

Can you simplify that?

Answer 4

yeah

Answer 5

@Kidthatbro8

Answer 6

225 / 3 ?

Answer 7

Yep, now divide that.

Answer 8

75 ?

Answer 9

Yes, so our slope is 75. Now we can plug that in along with one of our given points into point-slope form.

Answer 10

\(y - y_1 = m(x - x_1)\)

Where \(x_1\) is our x-value in our point, \(y_1\) is the y-value in our point, and \(m\) is our slope.

Let's use the point \((3, 285)\).

So in this case:

\(x_1 = 3\)
\(y_1 = 285\)
\(m = 75\)

Plug them in:

\(y - 285 = 75(x - 3)\)

Now simplify it, distribute 75 into the parenthesis, what do you get?

Answer 11

i got a very large number. 5400 ?

Answer 12

How did you get that?

Distributing 75 will just multiply it to 'x' and '-3'.

\(75 \times x =~?\)

\(75 \times -3 =~?\)

Answer 13

the first equation is a bit confusing, but the second one is -225, right ?

Answer 14

Yes.. \(75 \times x\) is the same thing as \(75x\).

Answer 15

So we get:

\(y - 285 = 75x - 225\)

Now we add 285 to both sides, what's -225 + 285?

Answer 16

60 ?

Answer 17

Yep, that gives us:

\(y = 75x + 60\)

So this is our equation..that takes care of Part A.

Answer 18

Now for Part B, we change it to function notation, do you know how to do that?

Answer 19

is that the f(x) thing ?

Answer 20

Yep, we just replace y with f(x).

So that gives us:

\(f(x) = 75x + 60\) in function notation..

Answer 21

That takes care of Part B.

Answer 22

Now for Part C, you will label the x-axis days, and the y-axis rent.

We can just plot the points (3, 285) and (6, 510) then draw a line through it.

Answer 23

That's all of your answers! :D

Answer 24

thank you so much ! ;v;

Answer 25

No problem.