Question

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

Answer 1

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-2y<=4` becomes `x-2y=4`.

Isolate `y` so that we have the equation in the form `y=mx+b`

`x-2y=4`.
`-2y=4-x`
`y=(4-x)/-2`
`y=-2+x/2`
`y=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.)
`2-2y<=4`
`-2y<=4-2`
`y>=2/-2`
`y>=-1`
We see that all y values that are located at the upper side of the slope are greater than -1, including the slope.

Answer 2

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

Explanation:

To solve this, you can temporarily change the `<=` to `=`. So the equation will now look like this:

`x - 2y = 4`

Now we can put the equation into the form `y = mx + c`:

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

`-y = -1/2x + 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 `<=` again, so we end up with:

`-y <= -1/2x + 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 `<= -1/2 xx 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 <= 3.5` which is true.

Hope this helps!