You go to an arcade and purchase a card with game credits. After playing 5 games you have 33 credits left. You play 4 more games and you have 21 credits left. Write an equation that represents the number of credits y on the cards after x games.

We will use slope-intercept form of equation to write our equation. The equation of a line in slope-intercept form is: [tex]y=mx+b[/tex], where m= Slope of the line, b= y-intercept.

To write the equation that represents the number of credits y on the cards after x games, we will find slope of our line.

We have been given that after playing 5 games we have 33 credits left. We play 4 more games and we have 21 credits left. So our points will be (5,33) and (9,21).

Let us substitute coordinates of our both given points in slope formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex],

[tex]m=\frac{21-33}{9-5}[/tex]

[tex]m=\frac{-12}{4}=-3[/tex]

Now let us substitute m=-3 and coordinates of point (5,33) in slope intercept form of equation to find y-intercept.

[tex]33=-3\cdot 5+b[/tex]

[tex]33=-15+b[/tex]

[tex]33+15=b[/tex]

[tex]48=b[/tex]

Upon substituting m=-3 and b=48 in slope-intercept form of an equation we will get,

[tex]y=-3x+48[/tex]

Therefore, our desired equation will be [tex]y=-3x+48[/tex].