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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!

Graphing ReviewGraph each line.

a) y = x + 2 b) x – 2y = 6

Graphing a Linear Inequality

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

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 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 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 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

- 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

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

When dealing with slanted lines

- If it is > or then you shade above
- If it is < or then you shade below the line

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!

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

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

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

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

Sketch a graph of y 3

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

- Complete the kuta worksheet

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

- Graph each inequality.
- Determine if the given point is a solution.
- Do # 1-3
- Check solution with your neighbor

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

- Write a letter to an absent student explaining what an inequality is and how to graph a system of inequalities?

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

Graphing ReviewUse 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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