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

Nov 30, 2017

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.
$x - 2 y \le 4$ becomes $x - 2 y = 4$.

Isolate $y$ so that we have the equation in the form $y = m x + b$

$x - 2 y = 4$.
$- 2 y = 4 - x$
$y = \frac{4 - x}{-} 2$
$y = - 2 + \frac{x}{2}$
$y = \frac{1}{2} x - 2$

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.)
$2 - 2 y \le 4$
$- 2 y \le 4 - 2$
$y \ge \frac{2}{-} 2$
$y \ge - 1$
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

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

#### Explanation:

To solve this, you can temporarily change the $\le$ to $=$. So the equation will now look like this:

$x - 2 y = 4$

Now we can put the equation into the form $y = m x + c$:

$- 2 y = - x + 4$
(We can make this better by dividing both sides by 2)

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

(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 $\le$ again, so we end up with:

$- y \le - \frac{1}{2} x + 2$

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 $\le - \frac{1}{2} \times x$ 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 $- 1 \le 3.5$ which is true.

Hope this helps!