Question

Claire has $300 Is an account. She decides she is going to take out $25 each month.

Answer 1

Total amount of Money in Claire account = $300

 Amount that,claire is going to take out each month = $ 25

As, she is going to take $25 ,each month ,the money in the account will form an Airthmetic sequence.

Sequence$S_{n}$

=300+(300-25)+(300-2×25)+(300-3×25)+............+(300-12×25)

                 =300+275+250+225+200+..................+25+0

First Term =300

Common Difference

                      =Second term - First term

                      =275 - 300

                      = -25

Recursive Formula

     $A_{n}=A_{n-1}-25\\\\A_{n}=\text{nth term}\\\\A_{n-1}=\text{(n-1)th term}$  

Explicit Formula

$A_{n}=A+(n-1)D\\\\A_{n}=300+(n-1)*25$

Graph will be like this

 Y-Intercept=300

 If $ 25 is taken out every month,

Number of month required to draw total of $ 300

   $=\frac{300}{25}\\\\=12$

So, equation of line can be derived using point slope form,as line cut x axis at (12,0) and y axis at (0,300).

     $\rightarrow \frac{x}{12}+\frac{y}{300}=1$

Answer 2

Recursive equation would be f(x+1) = f(x) - 25 with f(0) = 300

Explicit equation would be f(x) = -25x + 300

And graph would looks like this: