1. 6.5 Graphing Linear Inequalities

2. Graphing Linear Equations
A linear equation can be written in either slope-intercept form
Or in standard form
To graph we find the y-intercept then apply the slope

3. Graphing Inequalities
Inequalities are graphed by figuring where the solution starts and using an arrow to indicate the solution region

4. Linear Inequalities Equations
The solutions to a linear equation are the ordered pairs (x,y) which make the equation…
TRUE
The point ( 1, 2) is a solution to the equation
Inequalities So
The solutions to a linear inequality are the ordered pairs (x,y) which make the inequality…
TRUE

5. Solutions to Linear Inequalities
Which ordered pairs make the inequality true?
(0, 1)
(1, 0)
(10, -9)
(-9, 10)
In fact all of the points on the line make the inequality true.
But what about points like…
(3, 4), (0, 5) (-5, 8) (8, 9) (7, -4)

6. Solutions to Linear Inequalities (cont.)
We can replace the points that form the boundary line with a line
And we can replace all of the points in the region above the line with a shaded region
The graph of the line with a shaded region represents the graphical solution to the linear inequality above.

7. Graphing < or > Inequalities
If we have an inequality with a > or < symbol we have to adjust the graph
Just like on the number line if we want to indicate that the solution gets as close as possible but does not include a point we use an open circle
Since we are using a line instead of a point to represent the boundary we use a dotted line
The shaded region remains the same

8. Which Side to Shade?
Graph the line which represents the boundary of the inequality
Pick a test point to insert into the equation (usually the origin (0,0) if it is not on the line)
If the point makes the inequality TRUE shade the side which includes the point
If the points makes the inequality FALSE then shade the side that does not include the point
In this case
Is true so shade the side with the test point

9. Graph the Linear Inequalities
Pick (0, 0) as the test point

10. Graph the Linear Inequalities

11. Graph the Linear Inequalities