Question

b. What is the processing fee? The daily fee?The processing fee is $___ and the daily fee is $___ c. You cab spend no more that $1200 on the beach house rental. What is the maximum number of days you can rent the beach house?

Answer 1

We have the relationship between two variables that can be modeled by a line equation. We need first to determine the equation of the line. To do that can use the following equation for a line:

`y=mx+b`

Where "m" is the slope and b the y-intercept. To determine the slope "m" we use the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

Taking two points in the line:

`\begin{gathered} (x_1,y_1)=(2,246) \\ (x_2,y_2)=(4,450) \end{gathered}`

Replacing in the formula for the slope:

`m=(450-246)/(4-2)`

Solving the operations:

`m=(204)/(2)=102`

replacing in the equation for the line:

`y=102x+b`

To find the value of "b" we replace any point through which the line passes. Replacing (x,y) = (2,246):

`246=102(2)+b`

Solving the product:

`246=204+b`

subtracting 204 to both sides:

`\begin{gathered} 246-204=b \\ 42=b \end{gathered}`

Replacing in the line equation:

`y=102x+42`

The processing fee would be the initial fee and in the line equation, it is equivalent to the y-intercept therefore, the processing fee is $42. The daily fee is equivalent to the slope of the line, therefore, the daily fee is $102 per day.

If the total amount to spend is $1200 then replacing in the line equation:

`1200=102x+42`

Solving for "x" first by subtracting 42 to both sides:

`\begin{gathered} 1200-42=102x \\ 1158=102x \end{gathered}`

Dividing both sides by 102:

`\begin{gathered} (1158)/(102)=x \\ 11.4=x \end{gathered}`

Therefore, the number of days is 11.4.