Questions: Izumi is the scorekeeper for her school's basketball team at Florida State. Throughout the season, she has wondered if there is a relationship between the number of assists and number of rebounds. She collected data for each player and created the scatter plot shown. The equation y=-0.92 x+138.21 is fit to the data Izumi collected. Select ALL the statements that are true. A. Based on the model, there will be approximately 120 rebounds when 20 assists are made. B. The number of rebounds made decreased by 0.92 for each additional assist made C. The number of assists made decreased by 0.92 for each additional rebound made. D. The y-intercept represents the number of rebounds made when the number of assists are zero. E. The y-intercept represents the number of assists made when the number of rebounds are zero.

Solution Steps

Izumi collected data on the number of assists and rebounds for her school's basketball team and created a scatter plot. The equation of the line of best fit is given as \( y = -0.92x + 138.21 \).

The equation \( y = -0.92x + 138.21 \) represents the relationship between assists (x) and rebounds (y). The slope is -0.92, and the y-intercept is 138.21.

• Statement A: Based on the model, there will be approximately 120 rebounds when 20 assists are made.

  • Substitute \( x = 20 \) into the equation: \( y = -0.92(20) + 138.21 = -18.4 + 138.21 = 119.81 \). This is approximately 120 rebounds.
  • True

• Statement B: The number of rebounds made decreased by 0.92 for each additional assist made.

  • The slope of the equation is -0.92, which means for each additional assist, the number of rebounds decreases by 0.92.
  • True

• Statement C: The number of assists made decreased by 0.92 for each additional rebound made.

  • This is incorrect because the slope indicates the change in rebounds per assist, not the other way around.
  • False

Final Answer