Dr. Fowler CCM
Graphing Linear Inequalities
The graph of an inequality in two variables The graph of an inequality in two variables is the set of points that represent all is the set of points that represent all solutions of the inequality. solutions of the inequality.
The The BOUNDARY LINEBOUNDARY LINE of a linear of a linear inequality divides the coordinate plane into inequality divides the coordinate plane into two two HALF-PLANESHALF-PLANES. Only one half-plane . Only one half-plane contains the points that represent the contains the points that represent the solutions to the inequality. solutions to the inequality.
Graph an Inequality Graph an Inequality in Two Variables in Two Variables
Graphing LinearGraphing LinearInequalitiesInequalities
The boundary line will be a:– Solid line when ≤ and ≥ are used.
– Dashed line when < and > are used.Our graph will be shadedshaded on one
side of the boundary line to show where the solutions of the inequality are located.
Graphing Linear Inequalities Graphing Linear Inequalities
Graphing Graphing Boundary LinesBoundary Lines::
– Use a dashed line for < or >.Use a dashed line for < or >.
– Use a solid line for Use a solid line for ≤ or ≥.≤ or ≥.
Graph an InequalityGraph an Inequality
Graph the equation
STEPSTEP 11
Graph the inequality Graph the inequality y > 4x - 3 y > 4x - 3..
STEPSTEP 22
Test (0,0) in the original inequality.
STEPSTEP 33
Shade the half-plane that contains the point (0,0), because (0,0) is a solution to the inequality.
34 xy 34 xy
3)0(40
True
Graph an InequalityGraph an Inequality
Graph the equation
STEPSTEP 11
Graph the inequality Graph the inequality x + 2y ≤ 0..
STEPSTEP 22
Test (1,0) in the original inequality.
STEPSTEP 33Shade the half-plane that does not contain the point (1,0), because (1,0) is not a solution to the inequality.
02 yx 02 yx
0)0(21
False
2y = -x
y = -1 x
__ __2 2
2__
Graph an InequalityGraph an Inequality
Graph the equation
STEPSTEP 11
Graph the inequality Graph the inequality x + 3y ≥ -1..
STEPSTEP 22
Test (1,0) in the original inequality.
STEPSTEP 33Shade the half-plane that contains the point (1,0), because (1,0) is a solution to the inequality. 13 yx 13 yx
1)0(31
True
Plug in Zero’s to find x & y intercepts:
X intercept = -1Y intercept = -1/3
Graph an InequalityGraph an Inequality
Graph the equation
STEPSTEP 11
Graph the inequality Graph the inequality y ≥ -3..
STEPSTEP 22
Test (2,0) in the original inequality. Use only the y-coordinate, because the inequality does not have a x-variable.
STEPSTEP 33Shade the half-plane that contains the point (2,0), because (2,0) is a solution to the inequality. 3y
3y
3)0(
True
X intercept = noneY intercept = -3
Graph an InequalityGraph an Inequality
Graph the equation
STEPSTEP 11
Graph the inequality Graph the inequality x x ≤ -1..
STEPSTEP 22
Test (0,3) in the original inequality. Use only the x-coordinate, because the inequality does not have a y-variable.
STEPSTEP 33Shade the half-plane that does not contain the point (0,3), because (0,3) is not a solution to the inequality.
1x
1x
1)0(
False
y intercept = nonex intercept = -1
● 0,3
Excellent Job !!!Well Done
Stop NotesDo Worksheet