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Chapter P.3 Lines In A Plane

Chapter P.3 Lines In A Plane. Outline of Topics -Forms of a line -standard -slope-intercept -point slope -Slope -Horizontal & Vertical Lines -Parallel Lines & Perpendicular Lines -Interpolation & Extrapolation. Presenters- Greg Estabrooks & Tim Problem Solver- Amanda Johnson

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Chapter P.3 Lines In A Plane

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  1. Chapter P.3 Lines In A Plane Outline of Topics -Forms of a line -standard -slope-intercept -point slope -Slope -Horizontal & Vertical Lines -Parallel Lines & Perpendicular Lines -Interpolation & Extrapolation Presenters- Greg Estabrooks & Tim Problem Solver- Amanda Johnson Writer- Sarah Newton

  2. Review of Slope The Slope of a Line change in y change in x y2 - y1 x2 – x1

  3. Forms of a Line Standard Form Ax + By = C Point Slope Form y = mx + b Slope Intercept Form y - y1= m (x - x1) Short Cut Altering different equations to represent the same line. Standard Form to Slope Intercept m= -A/B b=C/B m=slope b= y-intercept Example Find the equation of the line that passes through the point (1,-2) and has a slope of 3. y-y1=m(x-x1) y-(-2)=3(x-1) y+2=3x-3 y=3x-5 m=slope x1= x coordinate of the point the line passes through y1= y coordinate of the point the line passes through

  4. Horizontal & Vertical Lines Horizontal Line -when the slope equals zero y = k k = all real numbers VerticalLine -when the slope is undefined x = k

  5. Parallel Lines Parallel Line - two lines are parallel if their slopes are equal Example y= 2/3x – 7/3 y – 4= 2/3 (x – 7) - Though they are different lines and in different forms, the slopes of these lines are equal and therefore parallel. Slope of l = m1 Slope of m = m2 m1 = m2

  6. Perpendicular Lines Perpendicular Line - two lines are perpendicular if their slopes are opposite reciprocals Example y= 2/3x – 7/3 y – 4= -3/2 (x – 7) - Though they are different lines and in different forms, the slopes of these lines are opposite reciprocals and therefore perpendicular. m1= -1/ m2

  7. Interpolation & Extrapolation • Interpolation • when the estimated point lies between two given points • Extrapolation • estimated point lies outside of the given points • the approximation of a point given a line l = best fit line a =the lower bound, smallest # in data b =the upper bound, largest # in data Interpolation- using the line of best fit to predict the value of x when it is between a and b a<x<b Extrapolation- a prediction using the line of best fit x<a or x>b

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