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Graphing Linear Inequalities
Graphing Linear Inequalities
Standard
A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane...and graph the solution...to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Step 1: Graph normally like a line.
Step 1: Graph normally like a line.
Step 2: Use a dotted line for < or >. Use a solid line for ≤ or ≥.
Step 2: Use a dotted line for < or >. Use a solid line for ≤ or ≥.
Step 3: Shade the region of solutions that make the inequality true.
Step 3: Shade the region of solutions that make the inequality true.
Example
Example
Graph y < (1/2)x + 1
- Identify your y-intercept: 1
- Plot a point on the y-axis at 1
- Identify your slope: (1/2)
- From the point you plotted, remember rise over run. So that means you go up 1, right 2.
- Are you using a solid or dotted line?
The dotted line means that we do not include values on that line as our solutions!
The dotted line means that we do not include values on that line as our solutions!
Shading
Shading
Since our equation is y < (1/2)x + 1, then our y values must be smaller and we shade below the line.
But if this isn't intuitive, here's another method:
- Choose any point. (0,0) is always nice to use when possible because the math is easy.
- Plug in your coordinate:
- 0 < (1/2)(0) + 1
- 0 < 1
- Is this true? Yes! So whichever side your coordinate was on--in this case we used (0,0)--then shade that side!
Example
Example
Graph x ≤ 3. Graph y > -2
Recall x ≤ 3 is a vertical "line".
Recall y > -2 is a horizontal line.
Keywords: linear inequalities, graphing
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