caseyparkey1
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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

Respuesta :

11x + y = 40 is the answer
cerverusdante

Answer

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: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where

[tex](x_{1},y_{1})[/tex] are the coordinates of the first point

[tex](x_{2},y_{2})[/tex] are the coordinates of the second point

We can infer from our points that [tex]x_{1}=0[/tex], [tex]y_{1}=40[/tex], [tex]x_{2}=1[/tex], and [tex]y_{2}=29[/tex]. So let's replace those values in our formula to find [tex]m[/tex]

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{29-40}{1-0}[/tex]

[tex]m=-11[/tex]

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

[tex]y-y_{1}=m(x-x_{1})[/tex]

[tex]y-40=-11(x-0)[/tex]

[tex]y-40=-11x[/tex]

[tex]y=-11x+40[/tex]

[tex]y+11x=40[/tex]

[tex]11x+y=40[/tex]