1. 6.5 Graphing Linear Inequalities

2. Graphing Linear Equations
A linear equation can be written in either ________________
Or in_____________
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…
_______
The point ( 1, 2)
___________________
Inequalities So
The solutions to a linear inequality are the ordered pairs (x,y) which make the inequality…
_______

5. Solutions to Linear Inequalities
Which ordered pairs make the inequality true?
______
____________________________________________________________
But what about points like…
____, _____, ______, ____, ____

6. Solutions to Linear Inequalities (cont.)
We can replace the points that form the boundary line with a _________________
And we can replace all of the points in the region above the line with a ________________
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 ________
Since we are using a line instead of a point to represent the boundary we use a ________________
The shaded region remains the same

8. Which Side to Shade?
Graph the line which represents the boundary of the inequality
Pick a __________to insert into the equation (usually ______________ if it is not on the line)
If the point makes the inequality ________shade the side which ___________ the point
If the points makes the inequality ___________ then shade the side that does not_________________
In this case
Is _____ so shade the side _____________________

9. Graph the Linear Inequalities
Pick ______as the test point
__________________________

10. Graph the Linear Inequalities
_____________________________

11. Graph the Linear Inequalities
______________________________