Algebra 1 Graphing Inequalities
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Choose Your Side
Graphing Inequalities

 
 So now we can graph equations like ...
 

 Y = 3X - 4

 
 without much problem.
 
 The graph of this line has a slope of 3 (the X coefficient).
 We can also see pretty easily that when X = 0, Y = -4.
 With a bit more work, we can also see that
 when X = 1, Y = -1 ...
 
  Y = 3X - 4
  Y = 3(1) - 4
  Y = 3 - 4
  Y = - 1
 
 So we can graph this puppy ...
 

 
 This wasn't too bad, but when some people see an equation
 that's only slightly different , they lose it completely.
 Say something like ...
 

Y > 3X - 4

 
 This thing is no big deal.
 
 Here's what you do with it.
 
 STEP 1:

 Pretend it's got an equal sign and graph it.

 
 STEP 2
 Now, pick some test point on the graph that's not on the line.
 and see if it makes the inequality true.
 (X = 0, Y = 0 is a good one if it's not on the line)
 
  Y > 3X - 4
  0 > 3(0) - 4
  0 > - 4          which is true!
 
 If the inequality is true when we put in the test point,
 then everything on the same side of the graph line
 as the test point gets shaded.
 
 If the inequality is NOT true when we put in the test point,
 then everything on the OTHER SIDE of the graph line
 from the test point gets shaded.
 

 
 STEP 3:
 The last thing to deal with is the line itself.
 If the equation uses or  then the line is solid
 If it uses > or < then the line is dotted.
 
 The solid lines mean that the points on the line
 are included in the area that makes the equation true.
 
 The dotted line means that all of the points 
 UP TO the points on the line on the shaded side
 make the equation true.
 

 Y > 3X - 4    uses   >

 
 so the line is dotted ...
 

 
 Let's try another one ...
 
 Example:

 Y < X

 
 STEP 1:

 Pretend it's got an equal sign and graph it.

 
 OK, the slope = 1. When X = 0, Y = 0. When X = 2, Y = 2 ...
 

 
 STEP 2
 Now, pick some test point on the graph that's not on the line.
 and see if it makes the inequality true.
 
 OK, we can't use (0,0) because it's on the line
 So let's try the point where X = 2 and Y = 3.
 

 
  Y < X
  3 < 2   nope, that's not true!
 
 That means the side we shade 
 is the side that the point is NOT on ...
 

 
 STEP 3:
 The last thing to deal with is the line itself.
 If the equation uses or  then the line is solid
 If it uses > or < then the line is dotted.
 
 The equation uses the less than symbol,
 so the equation has a dotted line ...
 

 

   copyright 2005 Bruce Kirkpatrick

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