Question

memorizing digits of pi
the equation for the line of best fit is $y = \frac{1}{5}x + 3$. according to the equation, which of these statements is true?
a typical student already knows approximately 3 digits of pi.
a typical student can memorize approximately 5 digits of pi in 1 minute.

Explanation:

Step1: Analyze the equation \(y = \frac{1}{5}x+3\)

In the linear equation \(y = mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept), for the equation \(y=\frac{1}{5}x + 3\), when \(x = 0\) (time \(x\) in minutes is \(0\)), \(y=\frac{1}{5}\times0+3=3\). Here, \(y\) represents the number of digits of \(\pi\) memorized.

Step2: Interpret the slope and \(y\) - intercept

The slope \(m=\frac{1}{5}\) means that for each increase of \(1\) in \(x\) (each additional minute), \(y\) (the number of digits memorized) increases by \(\frac{1}{5}\). The \(y\) - intercept \(b = 3\) means that when \(x = 0\) (before any time has passed for memorizing in this context), \(y=3\). This can be interpreted as a typical student already knows approximately \(3\) digits of \(\pi\).

Answer:

A. A typical student already knows approximately 3 digits of pi.