Solve the given inequality
Question:

Solve the given inequality $3 x+5 y<15$ graphically in two-dimensional plane.

Solution:

The graphical representation of $3 x+5 y<15$ is given by blue dotted line in the figure below.

This lines divides $x-y$ plane into two parts.

Select a point (not on the line), which lies on one of the two parts, to determine whether the point satisfies the given inequality or not.

We select the point as $(0,0)$

It is observed that $0+0<15$ or $0<15$ which is true.

Therefore, the solution for the given inequality excluding the points on the line. This can be represented as follows,