1. 0.3 Linear Inequalities Aug 29, 2012

2. Graphing x = # Ex. Graph x = -3 The x coordinate is -3 no matter what the value of y is. xy -30 1 2 3 Choose any value of y So, the graph of x = # is always a VERTICAL LINE

3. Graphing y = # Ex. Graph y = 2 The y coordinate is 2 no matter what the value of x is. xy 02 12 22 32 Choose any value of x So, the graph of y = # is always a HORIZONTAL LINE

4. Graphing Equations in Slope-Intercept Form Step 1: Using b, plot (0, b) on the graph. Step 2: From (0, b), plot the 2 nd point using the slope (rise/run). Step 3: Draw a line through the two points.

5. Graph 2 yx – = – Problem 1 1.Plot y-intercept (b) (0, -2) 2.From there rise 1 unit and go left 1 unit. or Go down 1 unit, go right 1 unit. 3. Connect 2 points with a line b (-1) m

6. Graph Problem 1 1.Plot y-intercept (0, 3). 2.From there rise 2 units and go right 3 unit. Place a point. or Go down 2 units, go left 3 units. 3. Connect 2 points with a line b m

7. Graphing Equations Standard Form Step 1: Find the x-intercept by letting y = 0 and solving for x. Plot (x, 0). Step 2: Find the y-intercept by letting x = 0 and solving for y. Plot (0, y). Step 3: Draw a line through the two points.

8. Example 2 Draw Quick Graphs Graph 3x + 2y = 12 x = 4 Solve for x. STEP 1 Find the x -intercept. 3x3x+ = 12 ( 02 ) Let y = 0. The x -intercept is 4, so plot the point (4, 0). y = 6 Solve for y. 2y2y+ = 12 ( 03 ) Let. x = 0 The y -intercept is 6, so plot the point (0, 6). STEP 2 Find the y -intercept. STEP 3 Draw a line through the intercepts.

9. Graphing a Linear Inequality 1.) Draw the boundary line: y=mx+b For > or <, dashed line For ≤ or ≥, solid line 2.) Shade the half plane. (Equations written in slope intercept form Above: > or ≥ Below: < or ≤ Above Below: Above Below Positive Slope Negative Slope Boundary line

10. 2. Shade the half plane (Equations written in standard form Ax+By = C) Test a point (x, y) not on the boundary line and see if it is a solution. If it is, shade the side that contains that point. If it is not, shade the other side.

11. Graphing Horizontal Line Inequality Ex: y > -2 Ex: y ≤ 3

12. Graphing Vertical Line Inequality Ex: x > -2 Ex: x ≤ 3

13. Example 3 Graph Linear Inequalities (y < mx + b) Graph +1. 2x2xy <

14. Example 3 Graph Linear Inequalities (Ax + By ≥ C) Graph – 8 3x3x2y2y ≥

15. More Examples y ≥ x

16. Graph More Examples y ≤ 3x3x –

17. Graph More Examples 2y2y < x + 6

18. Graph x- 2y > 4 More Examples