2.8-+Graph+Linear+Inequalities+in+Two+Variables

=A linear inequality in two variables can be written in different forms:= = = =** Ax + By < C **= =** Ax + By > C **= =** Ax + By ** ≤ ** C **= =** Ax + By ** ≥ ** C **= = =

=The Graph of a linear inequality in two variables is the set of all points in a cordinate plane the represent solutions of the inequality.= = = =A solution is an ordered pair (//x, y//) of a linear inequality in two variables if the inequality is true when the values of //x// and //y// are substituted into the inequality.=

a.) (6, -3) b.) (0,2) c.) (-2,-1) d.) (-3,5)

 * **Solution**
 * Ordered Pair** || **Substitute** || **Conclusion** ||
 * (6, -3) || 3( 6 ) + 4( -3 ) = 6 > 8 || Not a solution ||
 * (0, 2) || 3(** 0 ****)** + 4( 2 ) = 8 > 8 || Not a solution ||
 * (-2, -1) || 3( -2 ) + 4( -1 ) = -10 > 8 || Not a solution ||
 * (-3, 5) || 3( -3 ) + 4( 5 ) = 11 > 8 || Solution ||

=Links:= [] - How to do step by step

[] - Problem Questions

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= Avoid Errors! =

It is often convenient to use (0,0) as a test point. However, if (0,0) lies on the boundary line, you must choose a different test point.


==To graph a linear inequality in two variables (say, //x// and //y//), first get //y// alone on one side. Then consider the related equation obtained by changing the inequality sign to an equals sign. The graph of this equation is a line.==

==Finally, pick one point not on the line ((0, 0) is usually the easiest) and decide whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane==



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=**Assessment:**=