# How do you graph the line -x-3y=2?

Mar 27, 2016

See explanation.

#### Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

To build a graph (2 axis style $\to \text{ Cartesian}$) we need to be able identify the values in each axis. We can assign (within limits) any value we wish to $x$. So it does nor matter if this is imbedded within other value/actions. We must have the y value isolated (on its own).

$x$ is the independent variable. We can decide the value it takes.
$y$ is the dependant variable. Its value 'depends' on the value we assign to $x$.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Solving your question}}$

Given:$\textcolor{g r e e n}{\text{ } - x - 3 y = 2}$

To isolate the terms with $y$ in them (only 1) add $\textcolor{red}{x}$ to both sides

$\textcolor{g r e e n}{\text{ "-xcolor(red)(+x)-3y" "=" } 2 \textcolor{red}{+ x}}$

$0 - 3 y = 2 + x$

Multiply both sides by -1 giving

$+ 3 y = - x - 2$

Divide both sides by 3

$\frac{3}{3} \times y = - \frac{x}{3} - \frac{2}{3}$

But $\frac{3}{3} = 1$

$1 \times y = - \frac{x}{3} - \frac{2}{3}$

$\textcolor{b l u e}{y = - \frac{x}{3} - \frac{2}{3}}$ ...........................(1)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
You now have a choice. You can leave as is or you can factor out the $\frac{1}{3}$. This option would look like:

color(brown)(y=1/3(-x-2) or even ........................(2)

color(brown)(y=-1/3(x+2).........................(3)

$\textcolor{m a \ge n t a}{\text{Equations (1) ,(2) and (3) will all plot the same curve.}}$

To draw the graph you can build a table of values and then plot $x$ against $y$

The other option is to calculate the value of $x$ if $y = 0$ and the value of $y$ if $x = 0$