Transcript 2.6 Graphing linear Inequalities in 2 Variables

Warm-Up
Solve the linear system using substitution
1.  2 x  y  0
x y2
Solve the linear system using elimation.
2. -x  5 y  17
2x  10 y  34
Graphing linear
Inequalities
Checking Solutions
• An ordered pair (x,y) is a solution if it
makes the inequality true.
• Are the following solutions to:
3x + 2y ≥ 2
1. (0,0)
2. (2,-1)
3. (0,1)
3(0) + 2(0) ≥ 2
0≥2
Not a solution
3(2) + 2(-1) ≥ 2
4≥2
Is a solution
3(0) + 2(1) ≥ 2
2≥2
Is a solution
Solving for y
4. 2y < 8x + 10
Solid or Dashed??
5. 2x – y > -3
Solid or Dashed??
You Try!!
6. 2x – 5y > 15
Is the point (0, 0) a
Solution??
7.
-3x – 4y < -6
Is the point (2, 1) a
Solution??
To sketch the graph of a linear inequality:
1. Sketch the line given by the equation
(solid if ≥ or ≤, dashed if < or >). This line
separates the coordinate plane into 2
halves.
• In one half-plane – all of the points are
solutions of the inequality.
• In the other half-plane - no point is a
solution
2. You can decide which half to shade by
testing ONE point.
3. Shade the half that has the solutions to
the inequality.
Graph the inequality
8.
y ≥ -3/2x + 1
• Graph the line
• Before you connect the dots check to see if
the line should be solid or dashed
• solid if ≥ or ≤
• dashed if < or >
y ≥ -3/2x + 1
Step 1: graph
the boundary
(the line is
solid ≥)
Step 2: test
a point NOT
on the line
(0,0) is always
the easiest if it’s
Not on the line!!
(0) ≥ -3/2(0) + 1
0≥1
Not a solution So shade the other side of the line!!
9.
Graph: y < 6
10.
4x – 2y < 6
11.
2x – 6y > 18