Question

what is the vertical change from point A(0 , 0) to B(1 , 3)what is the horizontal change from point A(0 , 0) to B(1 , 3) what is the average rate of change?(i need an explanation cuz .. js cuz)

Answer 1

Solution:

The vertical change between two points is called the rise.

The vertical change (dy) is the difference between the y-coordinates of the points.

The horizontal change is called the run.

The horizontal change (dx) is the difference between the x-coordinates of the points.

The slope equals the rise divided by the run. The slope is also the average rate of change.

Given:

$\begin{gathered} A(0,0) \\ B(1,3) \end{gathered}$

where;

$\begin{gathered} x_1=0 \\ y_1=0 \\ x_2=1 \\ y_2=3 \end{gathered}$

a) The vertical change (dy) is calculated as shown below;

$\begin{gathered} =y_2-y_1 \\ =3-0 \\ =3 \end{gathered}$

Therefore, the vertical change (rise) is 3.

b) The horizontal change (dx) is calculated as shown below;

$\begin{gathered} =x_2-x_1 \\ =1-0 \\ =1 \end{gathered}$

Therefore, the horizontal change (run) is 1.

c) The average rate of change (slope) is given by;

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{rise}{\text{run}} \\ m=\frac{3}{1} \\ m=3 \end{gathered}$

Therefore, the average rate of change (slope) is 3.