Question

How do you get an inequality like `2x+y>2` in `y=mx+b` form?

Answer 1

Here is your inequality: `2x + y > 2`

Subtract 2x from both sides to obtain: `y > -2x + 2`

I think you were hoping that this new form would help you to graph the inequality and shade it properly!

So, use the slope m = -2 and the y-intercept (0,2) to draw your line as usual. Make the line dotted or dashed, so the reader knows NOT to include points on that line as "solutions" to this problem.

Now, you need to decide where to "shade" the graph. That means, what points will satisfy the inequality? Take a test point like (0,0) and see if it is true: `0 > -2(0)+2`
`0 > 2` is FALSE. So, do NOT shade on the side of the line where (0,0) is located.

Notice, I have placed a point on the same side of the graphed line as (0,0) would be, and the word "false" appeared! (I forced the calculator to test the point for me...)

Watch what happens when I move the point to the other side of the line (I would call it above the line):

All points in the blue shaded region would make the statement TRUE.
When your inequality is written so that it is solved for y, the inequality symbol literally points the way for you to shade! The > symbol means above, and the < symbol means below. If there is = attached to either symbol, then you must also include the line itself, by making it solid or darkened. Our dotted/ dashed lines shown do NOT include the line itself. Here is one last example for you to study: `y<=x-4`

I placed several points on the line, above and below the line. I indicated whether that point makes the inequality true or false. This time, the line is solid, indicating that points ON the line are TRUE.