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Section 1.1: Lines

by: ShesANotetaker

Section 1.1: Lines MAC 2233

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About this Document

These are the notes from the first lecture on 08/22/2016.
Methods of Calculus
Cory B. Ball
Class Notes
Math, Calculus, methods, MethodsOfCalculus




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This 2 page Class Notes was uploaded by ShesANotetaker on Tuesday August 23, 2016. The Class Notes belongs to MAC 2233 at Florida Atlantic University taught by Cory B. Ball in Fall 2016. Since its upload, it has received 35 views. For similar materials see Methods of Calculus in Mathematics at Florida Atlantic University.


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Date Created: 08/23/16
1.1 ­ Lines  ● ​ A l ​ ine is determined by two points.   ● A line is given by a formula.   ○ Point­slope form  ○ Slope­intercept form   Point Slope Formula   y − y  = m (x − x​ )   1​ 1​   ​ where m ​  is slope and x​  1​d y​  a1​ a point (​x​ ,1​​ 1​ ​Slope is the change of y, divided by the  change of x.     m = y​ 1​ y2   ​1 ​ x2     Slope­Intercept Formula  y = mx + b  ​ where b ​  is the y­intercept (0, b).      Horizontal lines have a slope of 0.   Vertical lines have the form X = X​  beca1​e their slope is undefined.     Types of lines:   ● Parallel   ● Perpendicular  Parallel Lines  Characteristics:   ● Never intersect  ● Same slope  ● Different intercepts     Example:   y  =  2x  + 5  These lines are parallel to each other because they  y  =  2x  −  4  have the same slope but not the same intercept. (If  they had the same intercept they would simply be  the same exact line).    Perpendicular Lines  Characteristics:   ● Lines meet and form 90° angles.       Perpendicular lines have slopes that when   m​ 1​ m​  2​­1  multiplied together equal to ­1. This is also    ​ known as being the n ​ egative reciprocal.     Example:     ⅙ ​ If ​y = ­  + 4, what is the perpendicular line at (0,9)?     ​ The perpendicular line is ​y = 6x + 9.     


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