Question

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 y - intercept

The equation of the line of best fit is $y=\frac{1}{5}x + 3$. In the slope - intercept form of a linear equation $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. When $x = 0$ (which represents the time of 0 minutes, or the initial state), we substitute $x = 0$ into the equation: $y=\frac{1}{5}(0)+3=3$. This means that when the time spent memorizing is 0 minutes, the number of digits of $\pi$ a typical student knows is 3. So the statement "A typical student already knows approximately 3 digits of pi" is related to the y - intercept and makes sense.

Step2: Analyze the slope

The slope $m=\frac{1}{5}$ in the equation $y=\frac{1}{5}x + 3$. The slope represents the rate of change of $y$ (number of digits memorized) with respect to $x$ (time in minutes). A slope of $\frac{1}{5}$ means that for each 1 - minute increase in time ($x$ increases by 1), the number of digits memorized ($y$) increases by $\frac{1}{5}$. So the statement "A typical student can memorize approximately 5 digits of pi in 1 minute" is incorrect because the slope is $\frac{1}{5}$, not 5.

Answer:

A typical student already knows approximately 3 digits of pi.