Graphing Linear Inequalities in Two Variables. LESSON ESSENTIAL QUESTION: How do you graph an inequality?. WARMUP. Complete Day 4 Warmup Problems. Shade , Shade, Shade, Shade It. http://teachertube.com/viewVideo.php?video_id=121267. Put the equations into y= mx+b form to graph!.
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LESSON ESSENTIAL QUESTION:
How do you graph an inequality?
Complete Day 4 Warmup Problems
Graphing a linear inequality is very similar to graphing a linear equation.
Where do you think the points that are y > x + 2 are located?
Where do you think the points that are y < x + 2 are located?
The line is the boundary of the two regions. The blue region is the “greater than” (>) area and the yellow region is the “less than” (<) area.
YOU WERE RIGHT!!
When the line that represents y = x + 2 is solid, not dashed, it means that the points on the line are included in the inequality. So we would state that the blue are can be represented byy ³ x + 2. And, the yellow couldbe represented by y £ x + 2.
When the line that represents y = x + 2 is dashed, it means that the points on the line are not included in the inequality. So we would state that the blue are can be represented by y > x + 2. And, the yellow could be represented by y < x + 2.
1. Change the inequality into slope-intercept form,
y = mx + b. Graph the equation.
2. If > or < then the line should be dashed.
If > or < then the line should be solid.
3. If y > mx+b or y >mx+b, shadeabove the line.
If y < mx+b or y <mx+b, shade belowthe line.
y =-3x + 2
b = 2
Test a point not on the line
0 -3(0) + 2
Instead of testing a point
If in y = mx + b form...
y ≥ 2x
Sketch a graph of x + y < 3
Step 1: Put into slope intercept form
y <-x + 3
Step 2: Graph the line y = -x + 3
Remember that when you multiply or divide by a negative number..FLIP THE INEQUALITY SIGN!!
3x - 4y > 12
-4y >-3x + 12
y < x - 3
Sketch a graph of y 3
Graph x < 2
Step 1: Start by graphing the line x = 2
Now what points would give you less than 2?
Since it has to be x < 2 we shade everything to the left of the line.
2y > 10-x
Use a graph to solve each system of equations.
a) y = x + 1 and y = -x + 3 b) 2x – y = 6 and y = x - 2