How do you graph the inequality # x – 2y > 4#, #x<4#?

1 Answer
MathFact-orials.blogspot.com
Dec 3, 2017

See below:

Explanation:

Let's first get the lines graphed. Then we can figure out which area to shade.

#x-2y=4#

I'll convert this to slope-intercept form:

#y=1/2x-2#

graph1{(x-2y-4)=0}

And #x=4#

graph1{(x-2y-4)(x-.000000001y-4)=0}

Now let's figure out the inequality. Both equations are either "less than" or "greater than" - we don't have an "equal to" in either line, and so the graph of both equations will be dotted.

With #x<4#, we want the shading to be to the left of the vertical line.

With #x-2y>4#, let's see if we want the origin to be a part of the solution or not:

#0-2(0)>4#

#0>4 color(white)(000)color(red)X#

So we want the shading to be below the diagonal line and to the left of the vertical line.

graph{(x-2y-4)(-x-.000000001y+4)(sqrt(5-(y+2)^2)/sqrt(5-(y+2)^2))>0}

(Since the graph doesn't want to behave, I've screened off the remaining lengths of the lines. In your graph, make sure they are there!)

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