Question

problem 8
determine the average rate of change of each
interval.
x(2,2)
y(8,3)
z(12,4)
x to z
x to y
y to z

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate \(X\) to \(Y\)

For \(X(2,2)\) and \(Y(8,3)\), \(x_1 = 2,y_1 = 2,x_2 = 8,y_2 = 3\).

$$ \frac{3 - 2}{8 - 2}=\frac{1}{6} $$

Step3: Calculate \(Y\) to \(Z\)

For \(Y(8,3)\) and \(Z(12,4)\), \(x_1 = 8,y_1 = 3,x_2 = 12,y_2 = 4\).

$$ \frac{4 - 3}{12 - 8}=\frac{1}{4} $$

Step4: Calculate \(X\) to \(Z\)

For \(X(2,2)\) and \(Z(12,4)\), \(x_1 = 2,y_1 = 2,x_2 = 12,y_2 = 4\).

$$ \frac{4 - 2}{12 - 2}=\frac{2}{10}=\frac{1}{5} $$

Answer:

\(X\) to \(Y\): \(\frac{1}{6}\), \(Y\) to \(Z\): \(\frac{1}{4}\), \(X\) to \(Z\): \(\frac{1}{5}\)