Question

a shop owner keeps track of how many quilts are sold (y) versus how many yards of fabric (x). calculate and interpret the slope.
slope = 3. the shop sells 3 times as many yards of fabric than quilts

Explanation:

Step1: Select two points

Select two points \((x_1,y_1)=(3,1)\) and \((x_2,y_2)=(9,3)\) from the graph.

Step2: Apply the slope formula

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
Substitute the values: \(m=\frac{3 - 1}{9 - 3}=\frac{2}{6}=\frac{1}{3}\).

Step3: Interpret the slope

The slope \(\frac{1}{3}\) means that for every 3 yards of fabric sold (\(\Delta x = 3\)), 1 quilt is sold (\(\Delta y=1\)).

Answer:

The slope is \(\frac{1}{3}\), which means that for every 3 yards of fabric sold, 1 quilt is sold.