Question

the equation for the line of best fit is ( y = -4x + 22 ). according to the equation, which of these statements is true? the student council used about 4 lemons per hour. the student council used about 22 lemons per hour.

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 \(y=-4x + 22\), \(x\) represents time (in hours) and \(y\) represents the number of lemons remaining.

Step2: Interpret the slope

The slope \(m=-4\). In the context of the problem, the slope represents the rate of change of the number of lemons with respect to time. Since the slope is \(- 4\), it means that for each unit increase in \(x\) (each hour), \(y\) (the number of lemons) decreases by \(4\). So the number of lemons used per hour is \(4\).

Step3: Interpret the \(y\)-intercept

The \(y\)-intercept \(b = 22\). In this context, when \(x = 0\) (at the start, \(0\) hours have passed), \(y=22\). So \(22\) is the initial number of lemons, not the number of lemons used per hour.

Answer:

The student council used about 4 lemons per hour.