The cost of renting video games from GAMES, INC. is shown in the table. Determine whether the cost is proportional to the number of games rented by graphing on the coordinate plane. Explain your reasoning.

1,3 2,5 3,7 4,9

1 answer

To determine whether the cost of renting video games from GAMES, INC. is proportional to the number of games rented, we can graph these points on a coordinate plane. The points given in your table are:

  • (1, 3)
  • (2, 5)
  • (3, 7)
  • (4, 9)

The first value in each pair represents the number of games rented, and the second value represents the cost in dollars.

Step 1: Plot the Points

We can plot the provided coordinates on a graph:

  • Point (1, 3): 1 game costs $3
  • Point (2, 5): 2 games cost $5
  • Point (3, 7): 3 games cost $7
  • Point (4, 9): 4 games cost $9

Step 2: Connect the Points

After plotting the points, we will see if they form a straight line.

Step 3: Check for Proportionality

For a relationship to be proportional, it should pass through the origin (0,0) and the ratio of the cost to the number of games should be constant.

Now, let's analyze the ratios for the points:

  • At (1, 3): Cost per game = 3/1 = 3
  • At (2, 5): Cost per game = 5/2 = 2.5
  • At (3, 7): Cost per game = 7/3 ≈ 2.33
  • At (4, 9): Cost per game = 9/4 = 2.25

Conclusion

The cost per game is not constant as we change the number of games rented—it's decreasing as the number of games increases. Additionally, the relationship does not pass through the origin because the cost of renting 0 games would logically be $0, but that’s a different interpretation as we cannot derive it from the given points.

Thus, the cost of renting video games from GAMES, INC. is not proportional to the number of games rented, as shown by both the graph not forming a straight line through the origin and the variable ratios of cost per game.