Question

Mary has a budget of $40 per month to spend on movies. She made a table showing the total amount of movie money she will have left after seeing the given number of movies.

Number of movies 0 1 2 3
Total amount of movie money left ($) 40 29 18 7
Which equation, in standard form, represents the relationship between the number of movies, x, and the amount of movie money Mary will have left, y?

11x−y= 4011x−y= 40

11x + y = 40

x + 11y = 40

x−11y= 40

Answer 1

11x + y = 40 is the answer

Answer 2

11x + y = 40

Explanation

We know from our table that when Mary has seen 0 movies her budget is $40, so our first point is (0, 40)

We also know that when she has seen 1 movie her budget is $29, so our second point is (1, 29)

To find our line equation, we first need to find the slope between our points. To do it, we are using the slope formula:
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

where

`(x_(1),y_(1))` are the coordinates of the first point

`(x_(2),y_(2))` are the coordinates of the second point

We can infer from our points that
`x_(1)=0`,
`y_(1)=40`,
`x_(2)=1`, and
`y_(2)=29`. So let's replace those values in our formula to find
`m`

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(29-40)/(1-0)`

`m=-11`

Now that we have our slope, we can use the point slope formula to find the equation of our line

`y-y_(1)=m(x-x_(1))`

`y-40=-11(x-0)`

`y-40=-11x`

`y=-11x+40`

`y+11x=40`

`11x+y=40`