A line is a function if
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A vertical line can be used to test whether or not a graph is a function.
The "vertical line test" will tell you if it is a function or not. The graph is not a function if it is possible to draw a vertical line through two points.
A linear function would be represented by a straight line graph, so if it's not a straight line, it's nonlinear
You use the vertical line test. If you can draw a vertical line though the graph and it intersects it only once, it is a function. If the line crosses the graphs more than once it is not.
For a 2-dimensional graph if there is any value of x for which there are more than one values of the graph, then it is not a function. Equivalently, any vertical line can intersect the a function at most once.