2.6 Linear Inequalities in Two Variables
A linear iinequality
nequality in two variables is an inequality that can be written in one of the
following forms:
Ax + By < C
Ax + By > C
Ax + By < C
Ax + By > C
An ordered pair (x, y) is a solut
olution
ion of a linear inequality if the inequality is true when
the values of x and y are substituted into the inequality.
Ex:
Ex: Determine if each point is a solution to 4x – 2y > 8.
a) (3, 3)
b) (−2, −9)
c) (0, 0)
Graphing Linear Inequalities
1.) Graph the “boundary” line.
• Use a solid line if < or >
• Use a dashed line if < or >
2.) Pick a test point on either side of the line, not a point directly on the boundary line.
If it is a solution, shade the region that contains the point.
**NOTE:
**NOTE: All points in shaded region are solutions to inequality.
Ex:
Ex: Graph each inequality.
d) y < 2
e) x > −1
f) 4x + 2y > 8
Your turn…
g) x > 5
j) 2x – 5y ≥ 10
h) y < – 4
k) 3x + y ≤ 6
i) y ≥ –x + 7
l) 3x – y < 3