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Published byElizabeth Burns Modified over 6 years ago

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2.5 Linear Equations

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Graphing using table Graphing using slope and y-intercept (section 2.4) Graphing using x-intercept and y-intercept (section 2.5) X-intercept y-intercept

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To find x-intercept, set y = 0, solve for x To find y-intercept, set x = 0, solve for y Ex1) 3x + 2y = 12 X-intercept: 3x + 2(0) = 12 3x = 12 x = 4 (4,0) Y-intercept: 3(0) + 2y = 12 2y = 12 y = 6 (0,6)

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Ex2) y = -4x + 5 Answer: x-intercept (5/4, 0) y-intercept (0, 5) Ex3) x + (1/2)y = -8 Answer: x-intercept (-8, 0) y-intercept (0, -16)

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To graph a linear equation, find x-intercept and y-intercept, plot them then connect the points. Ex: y = 2x – 4 we have x-intercept (2, 0) and y-intercept (0, -4) (2,0) (0,-4))

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Standard Form of Linear Equation: Ax + By = C Slope-Intercept Form: y = mx + b Point-Slope Form: y – y 1 = m (x – x 1 )

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Two lines are parallel if they have the same slope Ex: y = 3x + 4 y = 3x - 2 Two lines are perpendicular if the product of their slopes = -1 (or one slope is the opposite reciprocal of the other slope). Ex: y = (1/3) x y = -3x - 2

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Are these lines parallel, perpendicular, or neither? 1)y = (-3/2)x + 4 2y + 3x = 1 Answer: parallel (explain in class) 2)y = 5x 5y + 15 = x Answer: neither (explain in class) 3) x + 3y = 3 3x = 1 + y Answer: perpendicular (explain in class)

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Horizontal line: slope = 0 Ex: y = 4 or y = -2 Vertical line: slope is undefined Ex: x = 4 or x = -2 Y = 4 Y = -2 X = -2X = 4

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