math 101 - linear equations
math 101 - linear equations Math 101
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This page Class Notes was uploaded by Imee Oponda on Tuesday February 9, 2016. The Class Notes belongs to Math 101 at University of South Carolina taught by Schoening in Winter 2016. Since its upload, it has received 14 views. For similar materials see Intermediate Algebra in Math at University of South Carolina.
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Date Created: 02/09/16
Linear Equations A linear equation is an equation for a straight line These are all linear equations y 2X1 5X 63y Let us look more closely at one example Example y 2x1 is a linear equation The graph of y 2x1 is a straight line 0 When x increases y increases twice as fast hence 2x 0 When x is 0 y is already 1 Hence 1 is also needed 0 Soy2x1 Here are some example values x y2x1 4 y2x411 0 y2x011 1 y2x113 WZ3x Different Forms There are many ways of writing linear equations but they usually have constants like quot2quot or quotcquot and must have simple variables like quotxquot or quotyquot Examples These are linear equations yes y3x6 yes y23x1 yes y2x20 yes 5x6 yes y23 But the variables like quotxquot or quotyquot in Linear Equations do NOT have Exponents like the 2 in x2 Square roots cube roots etc Examples These are NOT linear equations no y220 no 3xy6 no x3216 SlopeIntercept Form The most common form is the slopeintercept equation of a straight line 3quot if It m or GradientlY Intercept Example y 2x 1 Our example from the top which is in SlopeIntercept form Slope m 2 Intercept b 1 PointSlope Form Another common one is the PointSlooe Form of the equation of a straight line r i yy1mxx1 Example y 3 1Arx 2 x12 y13 m General Form And there is also the General Form of the equation of a straight line Ax By C 0 A and B cannot both be 0 Example 3x 2y 4 0 A3 B2 C4 There are other less common forms as well As a Function Sometimes a linear equation is written as a function with fx instead of y y2x3 fx2x3 These are the same And functions are not always written using fx y2x3 wu2u3 hz223 These are also the same The Identity Function There is a special linear function called the quotIdentity Functionquot fx x And here is its graph It makes a 45 its slope is 1 It is called quotIdentityquot because what comes out is identical to what goes in In Out 0 0 5 5 2 2 etc etc Constant Functions Another special type of linear function is the Constant Function it is a horizontal line 3 it c x c E1 if fx C No matter what value of fx is always equal to some constant value
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