1. Linear Inequalities
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2. Linear Inequalities
A linear inequality describes a region of the coordinate plane that has a boundary line. (This region is called a half-plane.)
Every point in that region is a solution of the inequality.
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3. Solutions
When the inequality symbol has an “or equal to” (>, <, =) symbol, the boundary line is part of the solution.
The boundary line will be a solid line.
When the inequality symbol is just greater or less than (>, <), or not equal (≠), the boundary line is NOT part of the solution.
The boundary line will be a dashed line.
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4. If your equation is in the slope intercept form:
When you have > or >, you shade above the line.
When you have < or < , you shade below the line.
If the equation is NOT in slope intercept form… PUT IT THAT WAY!!
Remember…you should always check a point to see if it is in the solution set area.
Remember…you should always check a point to see if it is in the solution area.
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5. Example 1 Graph y < 3x – 2 Graph the line.
Remember that (0, –2) is the y-intercept.
Remember that 3 (or 3/1) is the slope.
Graph the line.
Decide if the line should be solid or dashed.
This would be dashed.
Decide whether to shade above or below the line.
This would be below the line.
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6. Example 1 Solution Graph y < 3x – 2 Graph the line --Dashed Shade
--Below the line
(0, 0)
Check a point
(0, 0)
y < 3x – 2
0 < 3(0) - 2
0 < -2 False—so not in shaded area
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7. Example 2: Write an inequality for the graph.
Write the equation of the line in slope-intercept form (y = mx + b).
- Find the y-intercept (0, b).
Find the slope (m) using rise over run.
(0,b)
Decide on the inequality symbol.
Since the shading is above the line, use greater than (>).
Since the line is solid, use the “or equal to” (>).
Solution: y > -2/3x + 4
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8. The End
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