Question

Calculating a rate of change

What is the vertical change form Point A to Point B?


What is the horizontal change from Point A to Point B ?


What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary?

Answer 1

Hello there. To solve this question, we'll have to remember some properties about rate of change.

Given the points A and B from a line, we want to determine the vertical change and the horizontal change between the points and then, using these values, determine the rate of change of the function (the line passing through them).

For this, we first find the coordinates of the points.

`A=(2,1)\text{ and }B=(4,2)`

The vertical change is the difference between the y-coordinates of the points, hence

`y(B)-y(A)=2-1=1`

The horizontal change is given by the difference between the x-coordinates of the points, therefore

`x(B)-x(A)=4-2=2`

The rate of change of this function is, finally, given by the ratio between the vertical (rise) and horizontal (run) changes of the function:

`(1)/(2)=0.5`

This is the rate of change of this function.