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) pls label parts

Answer 1

Part A) The equation in standard form is
`75x-y=60`

Part B) The equation in function notation is
`f(x)=75x+60`

Part C) The graph in the attached figure

Explanation:

Part A)

Let

x -----> the number of days

y ----> the total rent hat Maria has to pay for renting the coat

we have

(3,285) and (6,510)

Find the slope of the linear equation

`m=(510-285)/(6-3)=75(\$)/(day)`

Find the equation of the line into point slope form

`y-y1=m(x-x1)`

we have

`m=75`

`(x1,y1)=(3,285)`

substitute

`y-285=75(x-3)` ----> equation of the line into slope point form

Find the equation of the line into slope intercept form

`y=mx+b`

`y=75x-225+285`

`y=75x+60` ----> equation of the line into slope intercept form

Find the equation of the line into standard form

`Ax+By=C`

`y=75x+60`

`75x-y=60` -----> equation of the line into standard form

Part B) Write the equation obtained in Part A using function notation.

we have

`y=75x+60`

Convert to function notation

Let

f(x)=y

substitute

`f(x)=75x+60` ---> equation in function notation

Part C) Describe the steps to graph the equation obtained above on the coordinate axes

To graph the linear equation find out the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

`y=75(0)+60=60`

The y-intercept is the point (0,60)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

`0=75x+60`

`x=-60/75=-0.8`

The x-intercept is the point (-0.8,0)

To graph the line plot the intercepts ad join the points

see the attached figure