Question

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

Answer 1

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!)