Question

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

Explanation:

Step1: Recall the formula for rate of change

The rate of change (slope) formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Select two points from Taylor's table

Let's take \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1,25)\).

Step3: Calculate the rate of change

Substitute into the formula: \(m=\frac{25 - 0}{1 - 0}=\frac{25}{1}=25\).

Answer:

25