Question

50 - meter freestyle
the equation for the line of best fit is ( y = -\frac{3}{2}x + 49 ). according to the equation, which of these statements is true?
the coach predicts team members will swim the 50 - meter freestyle about 3 seconds faster for every 2 additional months on the team.
the coach predicts team members will swim the 50 - meter freestyle about 2 seconds faster for every 3 additional months on the team.

Explanation:

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

The equation of the line of best fit is in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. Here, \(y=-\frac{3}{2}x + 49\), and the slope \(m =-\frac{3}{2}\). The slope represents the change in \(y\) (swim time) with respect to the change in \(x\) (time on the team).

Step2: Interpret the slope

The slope \(m =-\frac{3}{2}=\frac{\Delta y}{\Delta x}\). The negative sign indicates that as \(x\) (time on the team) increases, \(y\) (swim time) decreases. When \(\Delta x = 2\) (2 additional months on the team), \(\Delta y=-\frac{3}{2}\times2=- 3\). This means that the swim time \(y\) decreases by 3 seconds when \(x\) (time on the team) increases by 2 months.

Answer:

The coach predicts team members will swim the 50 - meter freestyle about 3 seconds faster for every 2 additional months on the team.