Algebra
6.5 Graphing Linear Inequalities
Linear Inequality
• A linear inequality in 2 variables, x and y
• looks like a linear equation except that it has an inequality symbol instead of =
• Has an infinite number of solutions (x,y) that are points in one half of the coordinate plane
•Examples: y > 2x + 3y ≤ -3x - 1
Graph of Linear Inequality
Looks like this (shaded half-plane)
The solutions are all the points in the shaded region
Steps to Graphing(After Writing in Slope-Int.
Form)1. Graph the corresponding equation
• Use dashed line for > or <• Use solid line for ≥ or ≤
2. Shade the appropriate half-plane• Shade above for > or ≥• Shade below for < or ≤
3. Test (0, 0).
Example
• Graph 2x + y > 3(hint: rewrite the equation 2x + y > 3 in
slope- intercept form so that it is easy to graph.)
y > -2x + 3
dashed line
Example
• Graph y > -2x + 3shade above
Example• Test (0,0): 2x + y > 3 original
inequality
2(0) + 0 >30 > 3
(0, 0) is not a solution.It should not be in theshaded region.
It is not.
The correct half-plane is shaded.
You try!Graph 3y – x ≤ -12 Rewrite in SI form:
3y ≤ x - 12
y ≤ x - 4 1
3
What kind of line – dashed or solid?
Shaded above or below the line?
You try!Graph
Solid line, shaded below
y ≤ x - 4 1
3
Practice identifying above ( >, ≥) vs. below ( <, ≤)
shading
above
below
abovebelow
below = left
(lessthan)
above= right
(greater than)
above
below
y > 4 y < 6
x < 3
x > -2
Homework
pg. 363 # 39-56, 61-63
