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### Course: Integrated math 1>Unit 7

Lesson 2: Graphing two-variable inequalities

# Graphing two-variable inequalities

Sal graphs the inequality y<3x+5. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• When graphing, how do you know if you should use a solid line or a dotted line? Does the sign determine if it should be a solid or dotted line?
• if you have a less than or equal to/greater than or equal to the line will be solid
if you just have a greater than/less than then the graph of the line will be dashed
• how do you remember when to flip the sign? Like, sometimes it needs to flipped from < to > or vice versa.
• Try to remember that if you divide by a negative value then the inequality flips. For example, the equation: -3x < 12 becomes x > -4 because you have divided both sides by a negative value. To check if this is correct, replace x with a value that is less than -4 such as -5. Then evaluate the original equation to see if it makes sense. In this case if you insert a -5 in place of x in the equation -3x < 12 you get 15 < 12. This condition is not true so the solution can only be values of x that are > -4. Also, if you replace x with -4 in the original equation you get 12 < 12. This condition is not true either. So only values > -4 make the condition true. If you insert a -3 in place of x then the equation evaluates to 9 < 12. This condition is true and you know the inequality is facing in the right direction. Hope this helps. Jeff
• i still don't understand shading!
• on this video I'm having a serious issue at seeing the graph. can it be made bigger by any chance?
• If you hold the CTRL key and press + on your numpad, it will zoom in.
• I have a question regarding . How do you know which area will satisfy the inequality y < 3x+ 5 ? How do you know whether it's the area to the left of the dotted line or the area to the right of the dotted line?
• In the case that y<ax+b, then the shaded area will be "below" the dotted line, in the case that y>ax+b, then the shaded area will be "above" the dotted line.
• So if y < something, I draw below the dotted line, and if y > something, I draw above the dotted line? Thanks in advance...
• Yes, that is one way of thinking about it
• how does he know the shading
• The shading is determined by the inequality.
If the inequality is less than: y < mx+b, you shade below the line. If the shading is greater than: y > mx+b, you shade above the line.

If you want to confirm that you have shaded the correct side, pick a point from the side where you shaded. Then, test that ordered pair in the inequality. If it makes the inequality be "true", then you have shaded the correct side.

Hope this helps.
• how can you tell whether the line is shaded up or down? Im so confused
• If the inequality is in slope intercept form: y<mx+b or y>mx+b, then you can tell where to shade based upon the inequality.
-- If the inequality is "<", you shade below the line.
-- If the inequality is ">", you shade above the line.

You can also always pick a point on either side of the line and test it in the inequality.
-- If the point makes the inequality be true, then you shade that side.
-- If the point makes the inequality false, then you shade the opposite side.

Hope this helps.
• What if you had to graph in point slope form or another way besides slope intercept form? And how would you figure out what x equals in the first place?
• If you have it in point slope form, you have a point that you can graph, then use the slope to find additional points. In standard form, you can set x=0 to find y intercept and y=0 to find x intercept, then graph these two points.
If it is a linear function or linear inequality, the domain is all real numbers, so x could be anything.