4 Put the equations into y=mx+b form to graph! Graphing ReviewGraph each line.a) y = x b) x – 2y = 6
5 Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.
6 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?
7 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!!
8 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.
9 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 And, the yellow could be represented by y < x + 2.
10 Tell Your NeighborWhat 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 inequalityName 1 point in the solution setName 1 point NOT in the solution set
11 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 inequalityIf TRUE, you shaded correctIf FALSE, you shaded incorrectly
12 GRAPHING INEQUALITIES INEQUALITYSYMBOLTYPE OF LINE(dashed or solid)WHERE TO SHADE(above or below line)<>≤≥dashedbelowdashedabovesolidbelowsolidabove
20 -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 > 12y-3x x-4y > -3x + 12y < x - 3xBoundary Linem =b = -3
22 Graphing a Linear Inequality Sketch a graph of y 3
23 Graphing an Inequality in Two Variables Graph x < 2Step 1: Start by graphing the line x = 2Now what points would give you less than 2?Since it has to be x < 2 we shade everything to the left of the line.