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

Answer:

$y=-3x+48$

Step-by-step 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: $m=\frac{y_2-y_1}{x_2-x_1}$,

$m=\frac{21-33}{9-5}$

$m=\frac{-12}{4}=-3$

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 $y=-3x+48$.