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Linear Inequalities Page 178

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Formulas of Lines Slope Formula Slope Intercept Form Point Slope Form Ax + By = C Standard Form A,B,C ∈ℤ, A ≥ 0 Ax + By + C = 0 General Form a a a

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Slopes of Parallel Lines Parallel lines have the same slope. If they are both in slope-intercept form then only the y-intercept is different. Examples y=2x+6y-3=4(x+1) y=2x-8y+2=4(x+9)

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Slopes of Perpendicular Lines Perpendicular lines have slopes which are opposite reciprocals of each other. y=2x -2 is perpendicular to all lines y= -½ x + b for all values of b The product of the slopes of perpendicular lines is -1. 2 - ½ = -1

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A linear inequality in 2 variables is a graph that is half of the coordinate plane. Draw the solid or dotted line and shade on one side of it. Linear Inequalities

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< Is less than > is greater than ≥ is greater than or equal to ≤ is less than or equal to ≠ is not equal to or ≠ dotted line ≤ or ≥ solid line

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A solution of an inequality in two variables, x and y, is an ordered pair of real numbers with the following property: When the coordinates are substituted into the inequality, we obtain a true statement. Every ordered pair that is part of the solution “satisfies” the inequality.

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Determining if an ordered pair is a solution Substitute the ordered pair into both inequalities and see if the solutions are true. If both are true, the ordered pair is a solution. if the ordered pair gives a false solution in either equation, the ordered pair does not satisfy the system of inequalities. Is (3,1) a solution to the system of inequalities? y<2x-2 and y≥x-1

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How to graph A linear inequality is a region of a plane with a boundary line. The solutions of an inequality are all the points that make the inequality true and are represented by a shaded part of the graph. 1)Graph it like an equation by plotting points and determine how to connect the points with a solid or dotted line. 2)Then determine where to shade!

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Where do we shade?? If the equation is in slope intercept form with y on one side and everything else on the other, y> or y≥ shades above the line and y< and y≤ shade below the line. If you are not sure, pick a point not on the line and substitute it to see if it is a solution or not. If it is a solution shade there, if not, shade the other side.

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A linear inequality is a region of a plane with a boundary line. The solutions of an inequality are all the points that make the inequality true and are represented by a shaded part of the graph. y>5x+2 noticed the dotted line

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y≤2x+1 Notice the solid line

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y>4x-1 pick any point like (0,0) if it is true, shade on the left, if it is false, shade on the right where (0,0) is located).

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y>4x-1 pick a point (0,0) if it is true, shade on the left, false, shade on the right where (0,0) is located. 0>4(0)-1 0>-1 true

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(a) (b) (c) (d)

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Graphing > or < graph with a dotted line ≥ or ≤ graph with a solid line Then determine where to shade. Pick a test point and if the inequality is true for the test point, graph that side of the line.

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y<4x-1

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y≥-4x-3

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(a) (b) (c) (d)

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Practice Pages 180-181

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1)y > 0.5x – 4 (0,0), (8,2) are solutions (2, -4) 2)2x – 3y ≤ 10 (9,3) is a solution (3,-2),(-5,-7) 3) 4)

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Classwork/ 나우웤 열람실웤 /Homework page 183 - 187

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