The graph shows a line. The rate of change of the graph is 0.5 and the horizontal displacement is 2 units.
Given information:
The coordinates of point A is (2,1).
The coordinates of point B is (4,2).
While moving from point A to B, the coordinates of the point change from (2,1) to (4,2).
So, the horizontal displacement of the point is the change in x-coordinate which will be,
[tex]4-2=2[/tex]
So, horizontal displacement is of 2 units.
Similarly, the vertical displacement is 1 unit.
Now, the rate of change of the graph is simply the slope of the line shown in the graph.
So, the rate of change will be,
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\m=\dfrac{2-1}{4-2}\\m=0.5[/tex]
Therefore, the rate of change of the graph is 0.5 and the horizontal displacement is 2 units.
For more details, refer to the link:
https://brainly.com/question/18675172