Imagine a subscription to a service charges a onetime activation fee of $5 on top of $12 a month. This is one of the many examples that can be modelled on a graph. This particular subscription will follow a linear relation as the monthly rate stays at $12/month.
This is the essence of linear functions. When there is constant rate, there is a straight line on the graph.
These graphs are illustrated on a Cartesian plane. The Cartesian plane has 4 quadrants, which are divided by the x and y axis. As we move up and to the right, the x and y values increase. As we move down and to the left, the x and y values decrease. As an example, the equation $y=2x+1$ is pictured below.
Term  Definition  Example 

Vertex (Point) 

(0,1) 
Slope 

The slope in this case is 2. 
yintercept 

(0, 1) 
xintercept 

(0.5, 0) 