Question

Aaron has a budget of $100 per month to spend on lunch. He made a table showing the total amount of lunch money he will have left after the given number of lunches.

Number of lunches:0, 5, 10, 15
Total amount of lunch money left$ 100, 75, 50, 25

Which equation, in standard form, represents the relationship between the number of lunches, x, and the amount of lunch money Aaron will have left, y?

Answer 1

A line $y=mx+n$ passes through the points (0,100), (5,75), (10,50) and (15,25).

$x=0, y=100 \\y=mx+n \\100=m \times 0+n \\n=100 \\ \\x=5,y=75 \\y=mx+n \\75=m \times 5+100 \\-25=5m \\m=-5 \\ \\y=-5x+100$

Answer 2

5x + y = 100

5(5 lunches) is 25 arbitrary units

amount left after 5 is 75

25 + 75 = 100

each lunch is 5 dollars