3y-5x=-13

Great answer Ninja,

Grreat use of LaTex too!  (I answered your latex question for you as well)

I'm going to do it a different way (and I will practice some LaTex while I am at it)

3y-5x=-13

 $$\\If\; x=0\;\; then \;\;3y=-13 \;\;so \;\;y=\frac{-13}{3}=-4\frac{1}{3}\;\;(0,-4\frac{1}{3})\\\\
If\; y=0\;\; then \;\;-5x=-13 \;\;so \;\;x=\frac{13}{5}=2\frac{3}{5}\;\;\;(2\frac{3}{5},0)\\\\
\begin{array}{|c|c|c|}\hline
$x$&0&2\frac{3}{5}\\\hline
$y$&-4\frac{1}{3}&0\\\hline
\end{array}\\$$

FOR PEOPLE LEARNING LATEX

This is the code that I have used.

\\If\; x=0\;\; then \;\;3y=-13 \;\;so \;\;y=\frac{-13}{3}=-4\frac{1}{3}\;\;(0,-4\frac{1}{3})\\\\

If\; y=0\;\; then \;\;-5x=-13 \;\;so \;\;x=\frac{13}{5}=2\frac{3}{5}\;\;\;(2\frac{3}{5},0)\\\\

\begin{array}{|c|c|c|}\hline

$x$&0&2\frac{3}{5}\\\hline

$y$&-4\frac{1}{3}&0\\\hline

\end{array}\\

I drew the picture with GeoGebra

Are you wondering how you graph this?

To do this, you have to switch it to the slope intercept form.

The slope intercept form is y = mx + b, where m = slope and b = y intercept.

Let's work this out.

$$\begin{array}{rll}
3y -5x &=&-13\\
y- 5/3x &=& -13/3\\
y &=& 5/3x - 13/3\\
y &=& 5/3x -4 \frac{1}{3}
\end{array}$$

We can plot the point (0, -4 1/3) now, because the -4 1/3 tells us the y intercept.

Then, from that point, we can go up 5 and over 3 to the right. We do this because 5/3 tells us our slope, and it is written as up/over. I know to go 3 to the right because this is a positive slope.

If you had something like y = -5/3x + 2, you would go over 3 to the left, because that would be a negative slope.

Anyway, we go up 5 and over 3 to the right, then plot that point (put a dot there.) Now we have two points so we grab a ruler and draw a line through those two points. That's our graphed line!

Here's what this one will look like: