linear inequalities in two variables objectives: solve and graph a linear inequality in two...
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Linear Inequalities in Two Variables
Objectives: Solve and graph a linear inequality in two variables.
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A linear inequality in two variables, x and y, is any inequality that can be written in one of the forms below, where A ≠ 0 and B ≠ 0.
Ax + By ≥ C Ax + By > C Ax + By ≤ C Ax + By < C
A solution of a linear inequality in two
variables, x and y, is an ordered pair
(x, y) that satisfies the inequality. The
solution to a linear inequality is a region of the
coordinate plane and is called a half-plane
bounded by a boundary line.
Graphing Linear Inequalities
1. Given a linear inequality in two variables, graph its related linear equation.
• For inequalities involving ≤ or ≥, use a solid boundary line.
• For inequalities involving < or >, use a dashed boundary line.
2. Shade the appropriate region.
• For inequalities in the form of y ≤ mx + b or y < mx + b, shade below the boundary line.
• For inequalities of the form y ≥ mx + b or y > mx + b, shade above the boundary line.
• For inequalities in the form x ≤ c or x < c, shade to the left of the boundary line.
• For inequalities in the form x ≥ c or x > c, shade to the right of the boundary line.
Ex 1. Graph each linear inequality.
• a. y < x + 2
b. y ≥ -2x + 3
* c. y > -2x - 2
Dotted Line
d. y ≥ 2x + 5
e. -2x –3y ≤ 3
f. 3x – 4y ≥ 4
-4y≥-3x + 4
y ≤ ¾ x - 1
g. -5x – 2y > 4
-2y > 5x + 4
y < -5/2 x - 2
Dotted Line
Ex 3. Graph each linear inequality. x is a vertical line
and
y is a horizontal line
a. x > -2
b. y ≤ -1
c. x ≤ -2
d. y > -1 Dotted Line
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