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.

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- anonymous

Can any one help me

- mathstudent55

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.

- mathstudent55

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

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## More answers

- anonymous

Do I have to do slope formula

- anonymous

- mathstudent55

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

- anonymous

Yea I got 75 @mathstudent55

- anonymous

As my slope

- mathstudent55

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.

- anonymous

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

- anonymous

- mathstudent55

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

- anonymous

Ok wait @mathstudent55

- mathstudent55

ok

- anonymous

I got y= 75x + 60

- anonymous

- mathstudent55

\(\Large y - 285 = 75(x - 3)\)
\(\Large y - 285 = 75x - 225\)
\(\Large 75x - y + 60 = 0\)
Your equation is correct.
Whether your answer is correct or incorrect depends on what your problem interprets "standard form" as.

- mathstudent55

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

- anonymous

Ok and what about C

- mathstudent55

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?

- anonymous

No

- mathstudent55

|dw:1439496411311:dw|

- mathstudent55

|dw:1439496512385:dw|

- anonymous

What about the x

- mathstudent55

|dw:1439496561622:dw|

- mathstudent55

Now |dw:1439496743456:dw|that we have 2 points, we draw a line through them.

- mathstudent55

To do part C, you need to explain how to graph. You can use use the method I used above.

- anonymous

Ok thank you

- mathstudent55

Part C.
Set up a graph with units for x, 1, 2, 3, 4, etc.
For y, make each mark 50 units since the numbers are large in y.
Now plot the y-intercept on the y-axis. It is 60.
Then use the slope to find at least one more point.
Connect the points with the line and extend it.

- mathstudent55

|dw:1439496985892:dw|

- mathstudent55

You're welcome.

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