# Question #81faf

Nov 28, 2015

1. Rearrange the equation in the form $y = a x + b$
2. Insert two different x values and obtain two different y values
3. Plot the points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ and connect

#### Explanation:

First of all, you need to rearrange the equation to make it in the form: $y = a x + b$ (equation of a line, where $a$ is the slope and $b$ the y-intercept).

In this case, the easiest way to rearrange would be to pass the $- y$ on the other side of the equal sign, making it a $+ y$,
AND
to pass the $+ 6$ on the other side of the equal sign, making it a $- 6$.
That is:

$2 x - y = 6$
becomes
$2 x - 6 = y$

Great! This is what we want! $y = 2 x - 6$.
We have the equation of the line.
Now it is just a matter of putting at least 2 different values for x,
and obtain 2 values for y.
Let's use some super-easy numbers, say, $x = 0$ and $x = 1$.

For $x = 0$,
$y = 2 \cdot 0 - 6$ so this is $y = - 6$.

For $x = 1$,
$y = 2 \cdot 1 - 6$ so this is $y = - 4$

Here you go, you have now two points, (0,-6) and (1,-4) which you can plot on your graph, and use a ruler to trace the line.
You can of course use other values for x, giving you other values for y, and you will see that they all fall on the same line! (math is great!)
graph{((x)^2+(y+6)^2 - 1/50)((x-1)^2+(y+4)^2 - 1/50)(y-2x+6)=0 [-16, 16, -8, 8]}
(note that the line passes through points (0, -6) and (1, -4) )

I hope this helps and that I was clear enough. Understanding this thoroughly, you will be able to trace any line. You only have to remember to rearrange the equation in the form $y = a x + b$.

So summarizing:
1. Rearrange the equation in the form $y = a x + b$
2. Insert two different x values and obtain two different y values
(these will be the coordinates of your two points)
3. Plot the points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$
4. Connect the points!