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Graphing Linear Inequalities in Two Variables. LESSON ESSENTIAL QUESTION: How do you graph an inequality?. WARMUP. Complete Day 4 Warmup Problems. Shade , Shade, Shade, Shade It. http://teachertube.com/viewVideo.php?video_id=121267. Put the equations into y= mx+b form to graph!.

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slide1

Graphing Linear Inequalities in Two Variables

LESSON ESSENTIAL QUESTION:

How do you graph an inequality?

warmup
WARMUP

Complete Day 4 Warmup Problems

shade shade shade shade it
Shade, Shade, Shade, Shade It
  • http://teachertube.com/viewVideo.php?video_id=121267
graphing review

Put the equations into y=mx+b form to graph!

Graphing Review

Graph each line.

a) y = x + 2 b) x – 2y = 6

graphing a linear inequality
Graphing a Linear Inequality

Graphing a linear inequality is very similar to graphing a linear equation.

graphing inequalities
Graphing Inequalities

Where do you think the points that are y > x + 2 are located?

Where do you think the points that are y < x + 2 are located?

graphing inequalities1
Graphing Inequalities

The line is the boundary of the two regions. The blue region is the “greater than” (>) area and the yellow region is the “less than” (<) area.

YOU WERE RIGHT!!

graphing inequalities2
Graphing Inequalities

When the line that represents y = x + 2 is solid, not dashed, it means that the points on the line are included in the inequality. So we would state that the blue are can be represented byy ³ x + 2. And, the yellow couldbe represented by y £ x + 2.

graphing inequalities3
Graphing Inequalities

When the line that represents y = x + 2 is dashed, it means that the points on the line are not included in the inequality. So we would state that the blue are can be represented by y > x + 2. And, the yellow could be represented by y < x + 2.

tell your neighbor
Tell Your Neighbor
  • What does it mean to be a point in the solution of an inequality?
    • A point in the shaded area of the solution set that fits the inequality
  • Name 1 point in the solution set
  • Name 1 point NOT in the solution set
steps to graphing linear inequalities
Steps to Graphing Linear Inequalities

1. Change the inequality into slope-intercept form,

y = mx + b. Graph the equation.

2. If > or < then the line should be dashed.

If > or < then the line should be solid.

3. If y > mx+b or y >mx+b, shadeabove the line.

If y < mx+b or y <mx+b, shade belowthe line.

  • To check that the shading is correct, pick a point in the area and plug it into the inequality
    • If TRUE, you shaded correct
    • If FALSE, you shaded incorrectly
graphing inequalities4
GRAPHING INEQUALITIES

below

dashed

above

dashed

below

solid

above

solid

slide14

When dealing with slanted lines

  • If it is > or  then you shade above
  • If it is < or  then you shade below the line
slide15

Graph y -3x + 2 on the coordinate plane.

y

Boundary Line

y =-3x + 2

m =-3

b = 2

x

Test a point not on the line

test (0,0)

0 -3(0) + 2

Not true!

slide16

Graph y -3x + 2 on the coordinate plane.

y

Instead of testing a point

If in y = mx + b form...

Shade

up

Shade

down

Solid

line

x

>

<

Dashed

line

surfing with inequalities
Surfing with Inequalities

y ≥ 2x

  • Will the inequality “surf” splash over our surfer?
  • Step 1: Graph line
  • Step 2: Dashed or solid line?
  • Step 3: Shade above or below line?
  • Step 4: Verify a point
slide18

Using What We Know

Sketch a graph of x + y < 3

Step 1: Put into slope intercept form

y <-x + 3

Step 2: Graph the line y = -x + 3

example

STEP 1

6

STEP 3

4

STEP 2

2

5

Example:
slide20

Graph on the coordinate plane.

Remember that when you multiply or divide by a negative number..FLIP THE INEQUALITY SIGN!!

3x - 4y > 12

y

-3x -3x

-4y >-3x + 12

-4 -4

y < x - 3

x

Boundary Line

m =

b =-3

example1

STEP 1

6

4

STEP 3

2

5

Example:

STEP 2

slide22

Graphing a Linear Inequality

Sketch a graph of y  3

slide23

Graphing an Inequality in Two Variables

Graph x < 2

Step 1: Start by graphing the line x = 2

Now what points would give you less than 2?

Since it has to be x < 2 we shade everything to the left of the line.

homework
HOMEWORK
  • Complete the kuta worksheet
surfing with inequalities1
Surfing with Inequalities
  • Will the inequality “surf” splash over our surfer?
  • Decide if the shading of inequality (the surf) will splash over the surfer.

2y > 10-x

7 5 practice
7.5 Practice
  • Graph each inequality.
  • Determine if the given point is a solution.
  • Do # 1-3
  • Check solution with your neighbor
example2
Example:

STEP 1

STEP 2

STEP 3

classwork
CLASSWORK
  • Complete the surfing with inequalities wsht
  • Turn in for a graded classwork assignment
  • Be accurate with your graphing
  • Be careful when dividing by a negative #
absent student letter
Absent Student Letter
  • Write a letter to an absent student explaining what an inequality is and how to graph a system of inequalities?
graphing review1

The solution to a system of Equations is the POINT of INTERSECTION

Graphing Review

Use a graph to solve each system of equations.

a) y = x + 1 and y = -x + 3 b) 2x – y = 6 and y = x - 2

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