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)=}(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)=}(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