Question

hansen tracks the statistics of his favorite professional basketball player. this scatter plot shows how many shots the player took in some games this season and how many baskets the player made. it also shows the line of best fit. basketball games scatter plot with x - axis shots taken (2,4,6,8,10,12,14,16,18,20) and y - axis baskets made (1,2,3,4,5,6,7,8,9,10), line of best fit and data points the equation for the line of best fit is $y = \frac{4}{9}x + \frac{2}{3}$. according to the equation, which of these statements is true? if the player takes 22 shots, he would probably make about 10 baskets. if the player takes 24 shots, he would probably make about 14 baskets.

Explanation:

Step1: Analyze the first statement

We are given the equation of the line of best fit \( y=\frac{4}{9}x+\frac{2}{3} \). For the first statement, when \( x = 22 \) (shots taken), we substitute \( x = 22 \) into the equation.
\( y=\frac{4}{9}\times22+\frac{2}{3}=\frac{88}{9}+\frac{6}{9}=\frac{94}{9}\approx10.44 \approx 10 \) (rounded to a reasonable number of baskets).

Step2: Analyze the second statement

When \( x = 24 \) (shots taken), we substitute \( x = 24 \) into the equation.
\( y=\frac{4}{9}\times24+\frac{2}{3}=\frac{96}{9}+\frac{6}{9}=\frac{102}{9}=\frac{34}{3}\approx11.33
eq14 \)

Answer:

If the player takes 22 shots, he would probably make about 10 baskets.