How do you graph the line #y=3#?

1 Answer
May 22, 2016

Here is the graph of function #y=3#
graph{3+x*0 [-10, 10, -5, 5]}

Explanation:

Recall the definition of a graph of function #y=f(x)#.
Its graph is a set of all points #(x,y)# on the coordinate plane that satisfy the equation #y=f(x)#.

Obviously, all points #(x,y)# on the horizontal line crossing the #Y#-axis at coordinate #3# satisfy the equation #y=3#, regardless of its #X#-coordinate.

Any points #(x,y)# outside of this horizontal line has #Y#-coordinate not equal to #3# and, therefore, does not satisfy the equation #y=3#.

This proves that the described above horizontal line is the graph of function #y=3#.