SOLUTION: what does the inequality 2x-4y>-6 look like on a graph?

Question 5881: what does the inequality 2x-4y>-6 look like on a graph?
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
first find what 2x-4y=-6 looks like, since this will be a straight line you can plot/sketch. Then 2x-4y>-6 will be either the region above the line or the region below the line.

So, to stech the line, we need it in the form y=mx+c, so:

2x-4y=-6
-4y=-2x-6 or...
4y = 2x+6
y = (2/4)x + 6/4
--> y = (1/2)x + 3/2

so, we know the gradient is +1/2
and we know the line crosses the y-axis at y=3/2.

So, sketch that.

Now for your question...where is 2x-4y>-6? well, following through the same process:

2x-4y > -6
-4y > -2x-6 or...
4y < 2x+6 -- since we multiplied all terms by -1 (to swap all signs round) we swap the > into a <
y < (2/4)x + 6/4
--> y < (1/2)x + 3/2

so, where is y less than the straight line? Answer: below the line.

So we want the region below the line.

Jon.

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