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.

Part B: write the equation obtained in part A using function notation.

Part C: describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Answer 1

Can any one help me

Answer 2

She paid $285 for 3 days and
she paid $510 for 6 days.

They want the number of days to be x and the cost to be y.
That means we have two ordered pairs:
(3, 285)
(6, 510)

You need to write the equation of the line that passes through those two points.

Answer 3

Do you know how to find the equation of a line when you are given two points on the line?

Answer 4

Do I have to do slope formula

Answer 5

@mathstudent55

Answer 6

Correct. You need to find the slope of the line using the two given points.
Can you do that?

Answer 7

Yea I got 75 @mathstudent55

Answer 8

As my slope

Answer 9

Correct.
Here is the equation of a line given 2 points.
The fraction is the slope, so you can put the slope there.

\(\Large y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)\)

\(\Large y - y_1 = \dfrac{510 - 285}{6 - 3}(x - x_1)\)

\(\Large y - y_1 = 75(x - x_1)\)

Now just choose one of the points and replace \((x_1, y_1)\) in the formula with the coordinates of the point you chose.

Answer 10

What do you mean when you say replace ( X1, Y1) in the formula with coordinates

Answer 11

@mathstudent55

Answer 12

\(\Large y - \color{green}{y_1} = 75(x - \color{red}{x_1})\)

Use point \((\color{red}{x_1}, \color{green}{y_1})\) such as \((\color{red}{3}, \color{green}{285} )\)

\(\Large y - \color{green}{285} = 75(x - \color{red}{3})\)

Now just simplify the expression.

Answer 13

Ok wait @mathstudent55

Answer 14

ok

Answer 15

I got y= 75x + 60

Answer 16

@mathstudent55

Answer 17

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

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

\(\Large 75x - y + 60 = 0\)

Your equation is correct.
Whether your answer is correct or incorrect depends on what your problem interprets "standard form" as.

Answer 18

For part B you need function notation.
That simply means solve for y, which you already did.
Then replace \(y\) with \(f(x) \).

Answer 19

Ok and what about C

Answer 20

For part C, think of graphing the equation using the slope-intercept form:

y = 75x + 60

Do you know how to graph an equation directly from the slope-intercept form without finding ordered pairs?

Answer 21

No