Question

How do you graph this inequality on a coordinate plane 2x-3y<=6?

Answer 1

Do you know how to work a similar problem like:

Graph this equation on a coordinate plane: 2x - 3y = 6

Same thing but as an equality?

Answer 2

So I have to convert into slope intercept form first?

Answer 3

Yes, that's a good start... the line that comes from the equality is the "border" for the inequality, if that makes any sense.

Plot that line first...

Answer 4

So would it be y=2/3x-2? Plot that?

Answer 5

yes, good. But remember, it's really y >= (2/3)x - 2.

So it's "y greater than or equal to..."

The line you found in slope intercept is the "equal to" part... but then you shade all the part of the coordinate plane above that line to include the "y greater than..." part.

Answer 6

It would be a solid line right?
Okay, now as an example,
3x+6y>=12
Do I also put this in slope intercept form?

Answer 7

Yes, solid line when the inequality is a "greater than or equal to" or a "less than or equal to". The idea is that the line itself is part of the region that satisfies the inequality.

If you had an inequality with just > or <, then you are supposed to graph it as a dashed line instead, since the line itself is NOT part of the region that satisfies the inequality.

And also, yes, you are right... when you get something like 3x + 6y >= 12, first, convert it to slope intercept form.

Answer 8

Be really careful working with the inequality as you convert to slope intercept form. Remember that if you have to multiply or divide the whole thing by a negative number to convert a negative y term to a positive, you have to reverse the direction of the inequality.

Answer 9

I get what you're saying. Thank you for all of your help.

Answer 10

Glad to help... glad it made sense... :)