Lesson All About Graphing Inequalities

Source code of 'All About Graphing Inequalities'

This Lesson (All About Graphing Inequalities) was created by by mangopeeler07(462)

: View Source, Show
About mangopeeler07: I'm here to help kids like me understand math. I like helping people "get it". I can help with arithmetic, geometry, trigonometry, and algebra.

One concept in algebra that a lot of people have trouble with is graphing inequalities.  An inequality is basically an equation with the equal sign removed and replaced by < or >, or the variation of those which include half an equal sign under it.  Truth is, if you can graph a line, you can graph an inequality.  It's very simple:

---Suppose you have the inequality {{{y>x+3}}}.

Just graph the line for y=x+3, for a start.  Once you've done that, just simply shade the part of the graph ABOVE that line to show that y is more than that. But there is one more step.  Dot the line.  Make sure it is dotted, because that shows that y does not include that line, y is above that line and ONLY above that line.
Now if {{{y>=x+3}}}, you would just draw the line normally and shade. No dots.

---Suppose the inequality was {{{y<x+3}}}.

Again, graph the line for y=x+3.  Then dot it, then shade UNDER it this time to show that y is less than that.  Again, if {{{y<=x+3}}}, then you would just draw the line normally and shade. No dots.

---Now you've heard me say above and under the line, but what about if it were a vertical line, such as {{{x>4}}}?

Graph the line for x=4.  Then dot the line and shade TO THE RIGHT of the line, since x values get higher going right on the x axis.  Again, if it were {{{x>=4}}}, then, just draw the line normally and shade. No dots.

---What about {{{x<4}}}?

Again, draw the line for x=4, dot it, and shade TO THE LEFT of the line.  If it were {{{x <=4}}} , then again, just draw the line normally and shade. No dots.

That's the end of this lesson.  I hope this explanation made graphing inequalities much easier for you!