Question

push - ups and throwing distance
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: Recall the slope - intercept form of a 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 \(x\) (number of push - ups). Mathematically, if \(x_1\) and \(x_2\) are two values of \(x\) with \(x_2=x_1 + 1\), then \(y_1=1.5x_1+3\) and \(y_2=1.5(x_1 + 1)+3=1.5x_1+1.5 + 3\). The difference \(y_2 - y_1=(1.5x_1+1.5 + 3)-(1.5x_1+3)=1.5\).

Answer:

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