Question

taylor and emma sell hand - knit sweaters to raise money for charity. the tables show the total am each person raises, y, as a function of the number of sweaters knitted, x. taylor’s sweaters sold, x: 0, 1, 2, 3, 4, 5, 6; amount raised ($), y: 0, 25, 50, 75, , , . emma’s sweaters sold, x: 0, 1, 2, 3, 4, 5, 6; amount raised ($), y: 0, 15, 30, 45, , , . taylor’s rate of change: 25. how much does emma raise per sweater? find the rate of change. emma’s rate of change:

Explanation:

Step1: Recall the formula for rate of change

The rate of change (slope) for a linear function \(y = mx + b\) (where \(b = 0\) in this case since when \(x = 0,y=0\)) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Select two points from Emma's table

Take the points \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1,15)\).

Step3: Calculate the rate of change

Using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), substitute \(x_1 = 0,y_1 = 0,x_2=1,y_2 = 15\). Then \(m=\frac{15 - 0}{1 - 0}=15\).

Answer:

\(15\)