the number of points scored and the number of basketball games played. Determine the average points per game

Question

first point (0, 0) second point (3, 90) third point (5, 150) fourth point (7, 210)

Answer 1

To determine the average points per game, we first need to interpret the data points you provided. Each point is represented as \((x, y)\), where \(x\) is the number of games played, and \(y\) is the total number of points scored.

The points you provided are:

1. (0, 0): 0 games, 0 points
2. (3, 90): 3 games, 90 points
3. (5, 150): 5 games, 150 points
4. (7, 210): 7 games, 210 points

Now, we can calculate the average points per game. The average points per game can be calculated using the total points scored and dividing it by the total number of games played.

1. For \(x = 0\) to \(x = 3\) games:

   • Total points = 90
   • Total games = 3
   • Average = \( \frac{90}{3} = 30\) points per game

2. For \(x = 3\) to \(x = 5\) games:

   • Additional points = \(150 - 90 = 60\)
   • Additional games = \(5 - 3 = 2\)
   • Average for these games = \( \frac{60}{2} = 30\) points per game

3. For \(x = 5\) to \(x = 7\) games:

   • Additional points = \(210 - 150 = 60\)
   • Additional games = \(7 - 5 = 2\)
   • Average for these games = \( \frac{60}{2} = 30\) points per game

Putting this all together from 0 to 7 games:

• Total points = 210
• Total games = 7
• Average points per game = \( \frac{210}{7} = 30\)

Thus, the average points scored per game is 30 points per game.