Question

loaves of bread
the equation for the line of best fit is ( y=\frac{1}{10}x ). according to the equation, which of these statements is true?
about ( \frac{1}{10} ) of the loaves go unsold each day.
about 10 loaves are baked each day.

Explanation:

Step1: Analyze the equation \(y = \frac{1}{10}x\)

In the linear equation \(y = mx + b\) (here \(b = 0\)), \(y\) represents the number of loaves sold and \(x\) represents the number of loaves baked. The slope \(m=\frac{1}{10}\) means that for every \(x\) loaves baked, \(y=\frac{1}{10}x\) loaves are sold. So the number of unsold loaves is \(x - y=x-\frac{1}{10}x=\frac{9}{10}x\). The fraction of unsold loaves is \(\frac{x - y}{x}=\frac{\frac{9}{10}x}{x}=\frac{9}{10}\), and the fraction of sold loaves is \(\frac{y}{x}=\frac{\frac{1}{10}x}{x}=\frac{1}{10}\).

Step2: Check the second option

The equation \(y = \frac{1}{10}x\) does not give a constant value for \(x\) (the number of loaves baked). \(x\) can be any non - negative real number depending on the situation, so we cannot say that about 10 loaves are baked each day from the equation \(y=\frac{1}{10}x\)

Answer:

About \(\frac{1}{10}\) of the loaves go unsold each day.