Question

How do you sketch the set of solutions of the inequality `y-2x<=2` on the `xy` plane?

Answer 1

Draw the line of `y = 2x+2` with a solid line and shade below the line (to the right)

Explanation:

Treat the inequality in the same way as a straight line graph, keeping the `<=` sign.

Change it to y-intercept/gradient form:

`y <= 2x+2`

Now draw the line of `y = 2x +2`, by plotting points, or by using the y-intercept gradient method.

Draw the line using a solid line, because points ON the line are part of the solution.
To show the solutions to the inequality you have to decide which side of the line to shade for the wanted region.

Choose a point such as `(0,0)` which is easy to substitute.

Check whether the chosen point gives a true or false statement!

`0 <= 0+2` is TRUE, therefore this point lies in the required region.

A point such as `(-10,-10)` will give: `-10 <= -20+2`
This is FALSE and confirms that the shading should be on the other side of the line. graph{y<=2x+2 [-3.56, 16.44, -2.66, 7.34]}