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