Question

a linear function includes the points (2, 3) and (0, 8). what is the rate of change of the linear function? record the answer as an improper fraction (fraction greater than one) in lowest terms.

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) of a linear function between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Identify the points

Let \((x_1, y_1)=(2, 3)\) and \((x_2, y_2)=(6, 8)\).

Step3: Substitute into the formula

Substitute the values into the slope formula: \(m=\frac{8 - 3}{6 - 2}\).

Step4: Simplify the expression

Calculate the numerator and denominator: \(8 - 3 = 5\) and \(6 - 2 = 4\), so \(m=\frac{5}{4}\).

Answer:

\(\frac{5}{4}\)