Question

1. a shop owner keeps track of how many quilts are sold (y) versus how many yards of fabric (x). calculate and interpret the slope.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(3,1)\) and \((x_2,y_2)=(9,3)\).

Step2: Substitute the values into the formula

\(m=\frac{3 - 1}{9 - 3}=\frac{2}{6}=\frac{1}{3}\).

Step3: Interpret the slope

The slope \(\frac{1}{3}\) means that for every 3 - yard increase in fabric (\(x\)), the number of quilts sold (\(y\)) increases by 1.

Answer:

The slope is \(\frac{1}{3}\). It means that for every 3 - yard increase in fabric (\(x\)), the number of quilts sold (\(y\)) increases by 1.