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

2 Answers
Nov 30, 2017

Answer:

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

With the upper side shaded in.

Explanation:

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. We know that the y-intercept is -2, and we also know that we can plot the points by moving once upward and twice to the right.

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.

Nov 30, 2017

Answer:

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

Explanation:

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!