# How do you graph x+6y<=-5?

Mar 27, 2015

Whenever your equation contains a greater/lesser than OR equal to sign, you will have to shade whichever regions satisfy the equation on the graph.

To begin, you must get y on a side by itself.

$x - x + 6 y \le - x - 5$ this moves x to the other side.
$6 y \le - x - 5$ now you must divide both sides by 6 to completely isolate $y$
$y \le - \left(\frac{1}{6}\right) x - \left(\frac{5}{6}\right)$

Your $- \left(\frac{1}{6}\right)$ is the slope of the line, remember rise/run is your standard slope format. This means for every $1$ you rise by, you must go $- 6$ over on the x axis. You could also graph by going down $1$ on the y axis, and over $6$ on the x.

To begin your graph you must look at your y intercept, $- \left(\frac{5}{6}\right)$. Remember, this is the y intercept because if you plug in 0 for x in the original equation, you get #-(5/6).

From your y intercept, $- \left(\frac{5}{6}\right)$, and you use the slope. $- \left(\frac{1}{6}\right)$ to plot as many points as you desire.

After your points are plotted. Remember, you must check which side of your line to shade. Plug in a point above or below the line and check if the equation is true. If the equation is proven true with the example points, then the side with the correct points is shaded.