Chapter P.3Lines In A Plane

Presenters- Greg Estabrooks & TimProblem Solver- Amanda JohnsonWriter- Sarah Newton

Outline of Topics-Forms of a line

-standard-slope-intercept-point slope-Slope

-Horizontal & Vertical Lines-Parallel Lines & Perpendicular Lines-Interpolation & Extrapolation

The Slope of a Linechange in ychange in x

y2 - y1

x2 – x1

Review of Slope

Forms of a LineStandard FormAx + By = C

Point Slope Formy = mx + b

Slope Intercept Formy - y1= m (x - x1)

m=slopex1= x coordinate of the point the line passes throughy1= y coordinate of the point the line passes through

m=slopeb= y-intercept

Short CutAltering different equations to represent the same line.

Standard Form to Slope Intercept

m= -A/B b=C/B

ExampleFind 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-3y=3x-5

Horizontal & Vertical LinesHorizontal Line

-when the slope equals zero

y = kk = all real numbers

Vertical Line

-when the slope is undefined

x = k

Parallel LinesParallel Line- two lines are parallel if their slopes are equal

Slope of l = m1

Slope of m = m2

m1 = m2

Exampley= 2/3x – 7/3y – 4= 2/3 (x – 7)

- Though they are different lines and in different forms, the slopes of these lines are equal and therefore parallel.

Perpendicular Line- two lines are perpendicular if their slopes are opposite reciprocals

m1 = -1/ m2

Perpendicular Lines

Exampley= 2/3x – 7/3y – 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.

Interpolation & ExtrapolationInterpolation-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 linea =the lower bound, smallest # in datab =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 ba<x<b

Extrapolation- a prediction using the line of best fit x<a or x>b