Graphing Linear Inequalities in Two Variables
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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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Graphing Linear Inequalities in Two Variables

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Graphing linear inequalities in two variables

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 + 2b) 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


Graphing inequalities5

GRAPHING INEQUALITIES

>

<


Graphing linear inequalities in two variables

  • When dealing with slanted lines

  • If it is > or  then you shade above

  • If it is < or  then you shade below the line


Graphing linear inequalities in two variables

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!


Graphing linear inequalities in two variables

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


Graphing linear inequalities in two variables

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:


Graphing linear inequalities in two variables

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


Graphing linear inequalities in two variables

Graphing a Linear Inequality

Sketch a graph of y  3


Graphing linear inequalities in two variables

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 + 3b) 2x – y = 6 and y = x - 2


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