Consider the following graph
Recall that the slope is given by
To find the slope, we need to select any two points on the graph.
Let us select the points (0, 4) and (2, 1)
Let us substitute these points into the above slope formula
So, the slope of the line is -3/2
Recall that a linear graph has a constant slope no matter which points we select on the graph, we will end up with the same slope.
Let us verify this by finding the slope again with two different points on the graph.
Let us select the points (4, -2) and (6, -5)
Let us substitute these points into the slope formula
As you can see, the slope of the line is still -3/2
This proves that our graph is linear since it has a constant slope.