Lots a Loot Bank charges a monthly service fee and a fee per check, and the chart below shows your total monthly fees in relation to the number of checks issued per month.

Monthly service fee is like the fixed cost which is basically the y-value where graph crosses the y-axis.

From graph we see that graph crosses at 1 on y-axis so monthly service fee according to sample graph = $1

Now the per check fee works like slope of the line.

To find the slope we need two points so find any two points on the graph of line. I'm using points (1,0) and (4,3)

now slope can be found using formula

Hence per check fee will be $0.5 as per attached sample graph.

You can use same technique for the original graph given with this question.

Step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

Really long apparently