Question

Which of the above graphs represents a linear function?

Answer 1

A function of the form $y=ax+b,$ where $a$ and $b$ are constants, is called a linear function.

Also, the graph of a linear function is a straight line.

Graph 1:


The above graph is that of a linear function as it is a straight line graph.

Also, it is a function of the form $y=ax+b,$ where $a=0.$

Graph 2:


Graph 2 represents a linear function.

Graph 3:


Graph 3 is not a straight line and hence does not represent a linear function. However, it is made of two linear functions.

Graph 4:


Graph 4 does not represent a function as the $x$ value remains the same for all the $y$-values.

∴ Only graphs 1 and 2 represent linear functions.