Today:

Warm-UpGraphing

InequalitiesKhan Academy Due Tomorrow

Class Work

TGIF January11, 2013

Warm-Up

1.

2. The perimeter of a triangle is 51". The longest side is twice the length of the shortest. The third side is 3 inches longer than the shortest side. Write an equation then find the length of each side.

3. 4. What percent of 60 is 45?

5.

Objective- To graph inequalities on the coordinate plane.

Recall…Graph n < 3 on a number line.

-3 -2 -1 0 1 2 3 4

Tell whether the ordered pair is a solution of the inequality.

Identifying Solutions of Inequalities

(–2, 4); y < 2x + 1

Substitute (–2, 4) for (x, y).y < 2x + 1

4 2(–2) + 1

4 –4 + 14 –3<

(–2, 4) is not a solution.

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 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 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 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

Notes & Review

Shade the Solution Set

If the point makes the inequality

true, shade that side of the line. 

If the point does not make the

inequality true, shade the opposite

side of the line.

Notes & Review

Class Work:Pages 71-72; All

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

ProblemIf 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 nickelsLet 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