Question

What is the rate of change of the line through (2,3) and (3,8)?

Answer 1

The rate of change of a line is regarded as the slope/ gradient (m) of the line

The slope/ gradient (m) of the line moving through points (x₁,y₁) and (x₂,y₂) is given as

$\begin{gathered} \text{slope (m)=}\frac{y_2-y_1}{x_2-x_1} \\ \text{Where x}_1=2,y_1=3_{} \\ \text{and x}_{2=}3,y_2=8 \end{gathered}$

On substituting the above values in the formula above we will have the slope to be

$\begin{gathered} \text{Slope (m)=}\frac{8-3}{3-2} \\ \text{slope (m)=5/1} \\ \text{slope (m)=5} \end{gathered}$

Therefore,

The rate of change of the line through (2,3) and (3,8) is 5