The graph of the equation $y=mx+c$ does not pass through the origin." Justify the statement

Draw the graph of linear equations $y=x$ and $y=-x$ on the same cartesian plane. What do you observe?

Determine the point on the graph of the linear equation $2x+5y=19$, whose ordinate is $1\frac{1}{2}$ times its abscissa.

For what value of $c$, the linear equation $2x+cy=8$ has equal values of $x$ and $y$ for its solution?

Write linear equation such that each point on its graph has ordinate $3$ times its abscissa.