How do you graph #x+6y

Question

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

Savannah Anderson · Accepted Answer

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+6y<=-x-5# this moves x to the other side. 
#6y<=-x-5# now you must divide both sides by 6 to completely isolate #y#
#y<= -(1/6)x-(5/6)# Your #-(1/6)# 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, #-(5/6)#. 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, #-(5/6)#, and you use the slope. #-(1/6)# 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.

Hazel Anglin · Answer

undefined To graph the inequality $x + 6y \leq -5$, first graph the boundary line $x + 6y = -5$. To do this, find the x-intercept and y-intercept by setting $x = 0$ and $y = 0$, respectively. Then draw a dashed line through these points.

For the x-intercept:
$0 + 6y = -5$  
$y = -\frac{5}{6}$  
So, the x-intercept is $(-5/6, 0)$.

For the y-intercept:
$x + 6 \cdot 0 = -5$  
$x = -5$  
So, the y-intercept is $(0, -5)$.

Plot these points and draw a dashed line passing through them.

Since the inequality is $x + 6y \leq -5$, shade the region below the boundary line because it includes points that satisfy the inequality.

How do you graph #x+6y&lt;=-5#?

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