Question

ms. gupta challenged the students in her math class to see how many digits of pi they could memorize. this scatter plot shows how long her students spent memorizing digits and how many digits each student memorized. it also shows the line of best fit. 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 slope - intercept form

The equation of the line of best fit is $y=\frac{1}{5}x + 3$, which is in the form $y=mx + b$ where $m$ is the slope and $b$ is the y - intercept.

Step2: Interpret the y - intercept

The y - intercept $b = 3$. In the context of the problem, when $x = 0$ (i.e., when no time is spent memorizing), $y=3$. This means a typical student already knows approximately 3 digits of pi.

Step3: Interpret the slope

The slope $m=\frac{1}{5}$. It means that for every 1 - unit increase in $x$ (1 minute increase in time), $y$ (number of digits memorized) increases by $\frac{1}{5}$ digit, not 5 digits.

Answer:

A typical student already knows approximately 3 digits of pi.