<s>[INST] How can you quickly use the graph of $3x-6y=4$ to produce the graph of $3x-6y=10$? To start with, I am asked to graph the lines $3x-2y=k$ for $k=1,2,3$ and $4$.
I find that the equations produce different parallel lines.
For each line where $k=2,3$ and $4$, the coordinates points are $0.5k$ below the coordinates points of the line $3x-2y=1$.
If we let $x=0$, we can find the $y$-intercept of the lines.
\begin{align*}
-2y&=k\\
y &=\frac{k}{-2}
\end{align*}
and if we increase $k$ by $1$ we decrease $y$ by $0.5$.
\begin{align*}
-2y&=k+1\\
y &=\frac{k}{-2}-\frac{1}{2}
\end{align*}
I'm not certain the above logic suffices in quickly using the graph of $3x -6y = 4$ to produce the graph of $3x-6y=10$.
\begin{align*}
-6y&=4+6\\
y&=-\frac{2}{3}-1 \\
y&=-\frac{5}{3}
\end{align*}
Can my answer be improved?
 [/INST] Since the goal is to describe the relationship between the two lines quickly, I will give a one-sentence way to do this:
The difference between the graphs of $3x-2y=4$ and $3x-2y=10$ is that the graph of the latter equation is a dilation, centered at the origin, of the graph of the former by a factor of $10/4$.
That means that every point on the original graph "moves" to a point that is $2.5$ times farther away from the origin.
(The detailed explanation for why this is true is contained in Amaan M's answer.)
</s>