Question

story hours
the equation for the line of best fit is ( y = 3x + 1 ). according to the equation, which of these statements is true?
for each additional child at story hour, about 3 more books get checked out.
for every 3 additional children at story hour, about 1 more book gets checked out.

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 \(y = 3x+1\), \(x\) represents the number of children and \(y\) represents the number of books.

Step2: Interpret the slope

The slope \(m = 3\). The slope \(m=\frac{\Delta y}{\Delta x}\), which means for a unit change in \(x\) (in this case, when \(x\) increases by 1, i.e., when there is one additional child), \(y\) (the number of books) changes by \(m\) units.

Answer:

For each additional child at story hour, about 3 more books get checked out.