Question

feeding horses
the equation for the line of best fit is ( y = -4x + 48 ). according to the equation, which of these statements is true?
each additional volunteer decreases the time it takes to feed the horses by about 48 minutes.
each additional volunteer decreases the time it takes to feed the horses by about 4 minutes.

Explanation:

Step1: Analyze 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 \(y=-4x + 48\), \(m=-4\) and \(b = 48\).

Step2: Interpret the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). Here, \(x\) represents the number of volunteers and \(y\) represents the time. When \(x\) (number of volunteers) increases by \(1\) (\(\Delta x=1\)), \(y\) (time) changes by \(m\). Substituting \(\Delta x = 1\) into \(y=-4x + 48\), we get \(y_1=-4(x + 1)+48=-4x-4 + 48=(-4x + 48)-4=y - 4\).

Answer:

Each additional volunteer decreases the time it takes to feed the horses by about 4 minutes.