Post on 19-Jun-2015
Today:Warm-Up
Parallel & Perpendicular LinesSolving & Graphing Inequalities
Class Work
27
NotesAll Khan Due @ end of the day
Final Exam Grades Posted @ v6 MathKhan for this Week Posted
Alt.Khan Available NowNotebooks: 1st leave today, 2nd Tuesday,
3rd Wed., 4th Thursday.
Warm Up:1. Solve the inequality: -1 < < 34 > x and x > -6; write as one inequality
-6 < x < 4
2. Solve for x: 1 -
1 +
Eliminate both denominators. Hint: There are 2 terms in both the numerator and the denominator.𝒙−𝟐 1 - 𝒙−𝟐−𝟐
𝒙−𝟐+𝟐𝒙−𝟒
𝒙
A quick look at the 3rd quarter
Warm Up:
5. Graph the inequality: 2x + 3y > 12
x
y
2-2
(0,4)
(6,0)
3. Write an equation for a horizontal line
6. Write an equation for a line perpendicular to: x = 2y + 12.
4. Write an equation with an undefined slope
Objective- To graph inequalities on the coordinate plane.
Recall…Graph n < 3 on a number line.
-3 -2 -1 0 1 2 3 4
a. (4, 5); y < x + 1
Tell whether the ordered pair is a solution of the inequality.
y < x + 1 Substitute (4, 5) for (x, y).
Substitute (1, 1) for (x, y).
b. (1, 1); y > x – 7
y > x – 7
5 4 + 15 5 <
1 1 – 7>1 –6
(4, 5) is not a solution. (1, 1) is a solution.
Vocabulary:
Half-plane: The region of a graph on one side of a boundary.Boundary: A boundary of an inequality is a line that separates the coordinate plane into half-planes.
A solid line (shown), includes the points on the line. The inequality is < or >.
A dashed line does not include the points on the line. The inequality is < or >.
Graphing Linear Inequalities
Step 1
Solve the inequality for y (slope-intercept form).
Step 2
Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.
Step 3
Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer.
Class Notes & Practice Problems:
Graphing Linear Inequalities
Graph y > 3 on the coordinate plane.
x
y
x
y
Graph x < -2 on the coordinate plane.
Graphing Linear Inequalities
Graph y > -3x + 2 on the coordinate plane.
x
yBoundary Line
y = -3x + 2
m = -3
b = 2
Test a point not on the linetest (0,0)
0 > -3(0) + 2
Not true!
Graphing Linear Inequalities
Graph y -3x + 2 on the coordinate plane.
x
y
Instead of testing a point
If in y = mx + b form...
Shade up
Shadedown
Solid line
Dashed line
> <
Graphing Linear Inequalities
Graph the solutions of the linear inequality.5x + 2y >
–8 Step 1 Solve the inequality for y.Step 2 Graph the boundary
line and Use a dashed line for >. y = x – 4
Step 3: Test a point not on the line. Use (0,0) when you can.5(0) + 2(0) > -8, True or False?If true, include that point in your shading.
Graph on the coordinate plane.
3x - 4y > 12-3x -3x-4y > -3x + 12-4 -4
y < x - 33
4
m =
b = -3
3
4
Boundary Linex
y
Graphing Linear Inequalities
Problem
If you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have.
Let n = # of nickels
Let d = # of dimes
0.05 n + 0.10 d < 5.00
or 5 n + 10 d < 500
Graphing Linear Inequalities
5n + 10d < 500n d
0 50
100 0
0 10 20 30 40 50 60 70 80 90 100n
d
60
50
40
30
20
10
0
When dealing with angled lines,If the inequality is > or > ,then you shade
above
Graphing Linear Inequalities
If the inequality is < or < ,then you shade below
Class Work:See Handout