Warm Up # 1 1.The perimeter of a rectangle is 32. The length is 1 more than twice the width. What...
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Transcript of Warm Up # 1 1.The perimeter of a rectangle is 32. The length is 1 more than twice the width. What...
Warm Up # 1
1. The perimeter of a rectangle is 32. The length is 1 more than twice the width. What are the dimensions of the rectangle?
2. Solve the system:
123
32
yx
xy
Homework Check
Essential Question
How can we represent the solution to a system of linear inequalities?
GRAPHING LINEAR
INEQUALITIES
Step 1) Put the inequalities into slope-intercept form.
y = mx + bslope
y-intercept
We show the solution to a linear inequality with a graph.
Step 2) Graph the line
a) If the inequality is < or >, make the lines dotted.
b) If the inequality is < or >, make the lines solid.
Step 3) Shade the correct region of the graph:
a) Above the line b) Below the linefor y > or y . for y < or y ≤.
**This is because more then 1 ordered pair can be a solution!
Examples:
1) y > -5x + 4
Examples:
2) x < 4 3) y ≥ -3
SYSTEMS OF INEQUALITIES
We show the solution to a system of linear inequalities with a graph!
Steps to Graphing a System of Inequalities:1) Put the inequalities into slope-
intercept form.2) Decide if the lines should be dotted or
solid3) Shade above for y > or y , shade
below for y < or y ≤.4) Shade the overlapping section darker
to show where the solutions to both inequalities lie.
Example #1: a: 3x + 4y > - 4
b: x + 2y < 2
Put in Slope-Intercept Form:
a: dotted
shade above
b:dottedshade below
Graph each line, make dotted or solid and shade the correct area.
Example, continued:
3: 1
4 a y x 1
: 12
b y x
3: 1
4 a y x
1: 1
2 b y x
#2 Graph the system of
linear inequalities.
x ³ –1
y > x – 2
#3x > -2y < 6-2x + y > -5
#4 y ≥ -x + 4y < 3x - 2
#5
x – y > 37x – y ≤ -3
#6
7x + 2y < -10-x + 2y ≤ 11
Classwork: Solving Systems of Inequalities Worksheet
Homework:
Unit 7 TEST -