# 6.5 Graphing Linear Inequalities

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6.5 Graphing Linear Inequalities

Graphing Linear Equations
A linear equation can be written in either ________________ Or in_____________ To graph we find the y-intercept then apply the slope

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

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… _______

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

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.

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

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 _____________________

Graph the Linear Inequalities
Pick ______as the test point __________________________

Graph the Linear Inequalities
_____________________________

Graph the Linear Inequalities
______________________________

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