Inequalities and graphs example 1

Graph the following inequality.

$x+2y>8$

Subtract $x$ from both sides to get $y$ on its own.

$x-x+2y>8-x$

$2y>8-x$

Divide both sides by 2 to get $y$ on its own.

$(2y)/2>8/2-x/2$

$y>8/2-x/2$

$y>4-x/2$

$y>\-x/2+4$

First, let's calculate some points on the graph.

Now draw a graph and mark on the above points and don't forget to use just a dotted line.

Plot the line

Now pick a point NOT on the line:

Find the position not on the line using the coordinates

Choose $x=0$ and $y=3$

$y>4-x/2$

and $3>4-0/2$

$3>4$

This reads 3 is greater than 4 which is of course incorrect.

So this DOES NOT SATISFY THE INEQUALITY.

DON’T SHADE IT.

Do shade the other side.

If this does not satisfy the inequality shade the opposite side