2.8 Graphing Linear Inequalities in Two Variables
Graphing Vertical and Horizontal lines We graph the inequalities the same as
equations, but with a couple of differences….
Put in form of y = mx + b
Find the slope and the y-intercept
Dashed or Solid If an inequality has a < or >, then draw a
dashed line. If an inequality has a , then draw a
solid line. or
Shading < and is shaded below the line
> and is shaded above the line.
If you are not sure which side of the line to shade, plug in any point as a test. You need to use a point that is NOT on the line.
(0,0) are (1,1) are usually good test points to use, as long as the point you choose is not on the line.
Example: y < x + 3
Line is dashed because it is <,
The line is shaded below and to the right of the line.
Any and All of the points in the shaded area are part of the solution.
slope is 1, y intercept is at (0,3)
Example: y ≥ 2x -1
Line is solid because it is ≥,
Plug in (0,0) as a test point:0 ≥ 0 – 1 ---TRUE, so (0,0) is in the shaded area.Shaded above and to the left of the line.
slope is 2, y intercept is at (0,-1)
y > -x + 2
Plug in (0,0)
0 > 0 + 2
0 > 2NOT TRUE
Lines with Slope
1. Decide whether your line is solid or dashed.
2. Rewrite the inequality as an equation in y = mx + b form.
3. Graph using the y-intercept and slope.
4. Plug a test point {usually (0, 0)} to determine on which side of the line you should shade.
Classwork Practice
Page 118, #8-16
Graphing Absolute Value Inequalities
y < |x-2| + 3
This is in the formy = a |x-h| + k
So the vertex is(2,3) and the right side of the “V” has a slope of 1.
Since y < |x-2| + 3Shade below the graph
Graphing Absolute Value Inequalities
y ≥ ½ |x+2|
Graphing Absolute Value Inequalities
y > -2 |x-1| - 4
Classwork
Text page 118, #8-16 All, and #19-29 odd
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