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

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