It can be continuous or discrete.
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A continuous linear function produces a straight line graph that can be extended indefinitely in either direction. If the two ordered pairs are plotted on a graph then a straight line can be drawn joining these points. If that line is extended beyond both ends then there are no set limits and the function becomes continuous.
The graph will be a line.
Linear = Straight line! So, a graph of a linear relationship is a straight line.
the graph is called a line
If you can trace the graph without lifting your pencil then it is continuous.