Graphing Linear Inequalities in Two Variables graph a linear inequality in two variables model a...

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Transcript of Graphing Linear Inequalities in Two Variables graph a linear inequality in two variables model a...

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Graphing Linear Inequalities in Two Variables graph a linear inequality in two variables model a real life situation with a linear inequality. Slide 2 Recall Graph n < 3 on a number line. - 3 - 2 - 1 0 1 2 3 4 Slide 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. Slide 4 Graph x - 2 on the coordinate plane. x y Slide 5 Graph y > 3 on the coordinate plane. x y Slide 6 Graphing a Linear Inequality Sketch a graph of y 3 Slide 7 Some Helpful Hints If the sign is > or < the line is dashed If the sign is or the line will be solid When dealing with just x and y. If the sign > or the shading either goes up or to the right If the sign is < or the shading either goes down or to the left Slide 8 Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y When dealing with slanted lines If it is > or then you shade above If it is < or then you shade below the line Slide 10 Graph y - 3x + 2 on the coordinate plane. x y Instead of testing a point If in y = mx + b form... Shade up Shade down Solid line Dashed line > Graph on the coordinate plane. 3x - 4y > 12 - 3x - 4y > - 3x + 12 - 4 y < x - 3 m = b = - 3 Boundary Line x y Slide 12 Graph y - 3x + 2 on the coordinate plane. x y Boundary Line y = - 3x + 2 m = - 3 b = 2 Test a point not on the line test (0,0) 0 -3(0) + 2 Not true! Slide 13 Problem If you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have. Let n = # of nickels Let d = # of dimes 0.05 n + 0.10 d < 5.00 or 5 n + 10 d < 500 Slide 14 nd 0 50 1000 0 10 20 30 40 50 60 70 80 90 100 n d 60 50 40 30 20 10 0 Slide 15 Graphing Absolute Value Inequalities Slide 16