Question

the varsity basketball team members at galileo high school participated in a 4 - week training program designed to improve their free - throw percentages. this scatter plot shows some of the team members percentages at different times during the training program along with the line of best fit. free - throw percentages the equation for the line of best fit is y = 4.8x + 33.4. according to the equation, which of these statements is true? before the training program started, a typical team member made about 33% of their free throws. over 1 week of training, a typical team member improved by about 33%.

Explanation:

Step1: Analyze the line - of - best - fit equation

The equation of the line of best fit is $y = 4.8x+33.4$, where $y$ is the percent of free - throws made and $x$ is the number of weeks of training.

Step2: Consider the initial condition

When the training program started, $x = 0$. Substitute $x = 0$ into the equation $y=4.8x + 33.4$. We get $y=4.8\times0 + 33.4=33.4\approx33$. This means that before the training program started (at $x = 0$ weeks), a typical team member made about 33% of their free - throws.

Step3: Consider the improvement per week

The slope of the line is 4.8. This means that for each additional week of training ($x$ increases by 1), the percent of free - throws made ($y$) increases by 4.8%, not 33%.

Answer:

Before the training program started, a typical team member made about 33% of their free throws.