Question

the equation for the line of best fit is ( y = -2x + 48 ). according to the equation, which of these statements is true? the number of people who sign up for a bike ride decreases by about 2 people for each additional mile. the number of people who sign up for a bike ride decreases by about 48 people for each additional mile.

Explanation:

Step1: Recall the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=-2x + 48\), \(m=-2\) and \(b = 48\).

Step2: Interpret the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). Here, \(x\) represents the distance (in miles) and \(y\) represents the number of participants. When \(x\) (distance) increases by \(\Delta x = 1\) (one additional mile), \(y\) (number of participants) changes by \(\Delta y=m\times\Delta x\). Substituting \(m=-2\) and \(\Delta x = 1\), we get \(\Delta y=-2\times1=-2\).

Answer:

The number of people who sign up for a bike ride decreases by about 2 people for each additional mile.