Question

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.

Answer 1

`y=-3x+48`

Explanation:

We will use slope-intercept form of equation to write our equation. The equation of a line in slope-intercept form is:
`y=mx+b`, 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:
`m=(y_2-y_1)/(x_2-x_1)`,

`m=(21-33)/(9-5)`

`m=(-12)/(4)=-3`

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

`33=-3\cdot 5+b`

`33=-15+b`

`33+15=b`

`48=b`

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

`y=-3x+48`

Therefore, our desired equation will be
`y=-3x+48`.