LESSON ESSENTIAL QUESTION: 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 Review Graph 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 by y ³ x + 2. And, the yellow could be 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, shade above the line. If y < mx+b or y < mx+b, shade below the 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 INEQUALITIES INEQUALITY SYMBOL TYPE OF LINE (dashed or solid) WHERE TO SHADE (above or below line) < > ≤ ≥ dashed below dashed above solid below solid above

GRAPHING INEQUALITIES SHADE UP SHADE BELOW SOLID LINE DASHED LINE ≥ ≤ > <

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. 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

Step 1: Put into slope intercept form 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

STEP 1 Example: STEP 3 STEP 2 6 4 2 5

-3x -3x -4y > -3x + 12 -4 -4 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

STEP 1 Example: 6 4 2 5 STEP 2 STEP 3

Graphing a Linear Inequality 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

Example: STEP 1 STEP 2 STEP 3

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 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