How do you graph the inequality #x - 2y

Question

How do you graph the inequality #x - 2y<=4#?

Savannah Anderson · Accepted Answer

The graph should look like this: graph{-2+x/2 [-10, 10, -5, 5]}

With the upper side shaded in.

First, we treat the inequality as an equation. #x-2y<=4# becomes #x-2y=4#. Isolate #y# so that we have the equation in the form #y=mx+b# #x-2y=4#. #-2y=4-x# #y=(4-x)/-2# #y=-2+x/2# #y=1/2 x-2# We graph this because we know that the y-intercept is -2 and that the points can be plotted by making two rightward movements and one upward movement. We know plug in a x value in the inequality.(Let's try 2.) #2-2y<=4# #-2y<=4-2# #y>=2/-2# #y>=-1# We see that all y values that are located at the upper side of the slope are greater than -1, including the slope.

Kennedy Adams · Answer

graph{-2y <= 4 - x [-10, 10, -5, 5]}

To solve this, you can temporarily change the #<=# to #=#. So the equation will now look like this: #x - 2y = 4# Now we can put the equation into the form #y = mx + c#: #-2y = -x + 4# (We can make this better by dividing both sides by 2) #-y = -1/2x + 2# (You can draw the graph now BUT if the sign is #<# or #># the graph line must be dashed) To shade the area we need to change that #=# to #<=# again, so we end up with: #-y <= -1/2x + 2# A good way to see which side of the graph to shade is to plug in a coordinate above and below the graph line. If the equation is true (meaning the #-y# coordinate is #<= -1/2 xx x# coordinate) then that is the side you should shade. In this case, you need to shade the top of the graph as trying the coordinate (1,1) gives #-1 <= 3.5# which is true. Hope this helps!

Genesis Allen · Answer

undefined To graph the inequality $ x - 2y \leq 4 $, follow these steps:

1. Rearrange the inequality to solve for $ y $: 
   $ y \geq \frac{x}{2} - 2 $.
2. Graph the line $ y = \frac{x}{2} - 2 $ (dotted line because it's "or equal to").
3. Since it's $ y \geq \frac{x}{2} - 2 $, shade the region above the line, including the line itself.

How do you graph the inequality #x - 2y&lt;=4#?

How do you graph the inequality #x - 2y<=4#?