Question

the equation for the line of best fit is $y = 1.5x + 3$. according to the equation, which of these statements is true? a typical student can be expected to throw a football about 3 yards farther for each additional push - up completed. a typical student can be expected to throw a football about 1.5 yards farther for each additional push - up completed.

Explanation:

Step1: Analyze the linear equation

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the given equation \(y = 1.5x+3\), \(x\) represents the number of push - ups and \(y\) represents the throwing distance.

Step2: Interpret the slope

The slope \(m = 1.5\). In the context of the problem, the slope represents the change in \(y\) (throwing distance) for a unit change in \(x\) (push - ups). So, for each additional push - up (\(\Delta x = 1\)), the change in throwing distance \(\Delta y=m\times\Delta x\). Substituting \(m = 1.5\) and \(\Delta x = 1\), we get \(\Delta y=1.5\times1 = 1.5\)

Answer:

A typical student can be expected to throw a football about 1.5 yards farther for each additional push - up completed.