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

See below:

#### Explanation:

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

$x - 2 y = 4$

I'll convert this to slope-intercept form:

$y = \frac{1}{2} x - 2$

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

$0 - 2 \left(0\right) > 4$

$0 > 4 \textcolor{w h i t e}{000} \textcolor{red}{X}$

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!)