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Two-variable inequalities from their graphs

Sal is given a graph and he analyzes it to find the two-variable inequality it represents. Created by Sal Khan and Monterey Institute for Technology and Education.

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• You can test out if the point works by filling in the x and y values of the equation with any point on the graph. I choose 0,0 because it's so easy. If the test with 0,0 is true, then the shaded region includes the point 0,0, and if it's false, shade the opposite region which doesn't include the point 0,0.
• Do you flip the inequality sign when multiplying or dividing by a POSITIVE number as well? Or is this rule only applicable to negative multiplication/devision.
• the inequality sign flips only when we multiply or devide any term with or by any negative number.
• At , how did Sal know from the question that the inequality would represent the area above the line and not below it?
• If the inequality is greater than, you shade above the line. If the inequality is less than, you shade below the line. Since the graph is shaded above this line, this is the portion that Sal needs to work with.
• what do the dotted and full lines stand for?
• Dotted (or dashed) lines mean that everything on the line does not count as part of the solution (using the < or > inequalities). Solid (or full) line means that the points on the line do count as part of the solution (using the ≥ or ≤ inequalities). These are related to the closed circles (count) and open circles (does not count) used on the number line if you are one variable instead of two.
• How do you figure out if its greater than or less than
• If y is on the left, then > or ≥ is above the line (in special case of vertical line such as x=4, to the right of the line) and < or ≤ is below the line.
• If this man has kids they are gonna be the smartest beings alive.
• sorry I'm really confused on how you got the greater than or less then symbols. if there is a big portion of the graph shaded does that mean it's greater than or less than? I already know if the line when the line is greater than or equal to or less than. when the line is solid its greater than or equal to or when the line is dashed its less than or greater than. if you can make a simpler way to help me remember which inequality to put that would be really helpful thank you
• Having a big portion or small portion shaded does not regard whether the symbol has to be greater than or less than.
Think of it this way: If the shaded part is above the line drawn, the sign is greater than/greater than or equal to. If the shaded part is below, it is less than/ less than or equal to. So phrase it in your mind: "above greater" "below less"
Hope this helps!
• Why is the inequality about everything above the line and not about everything below the line?
• because y ≥ the equation, not ≤ to the equation