CST 504 Linear Equations
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This document discusses linear equations and functions. It defines the slope-intercept form of a linear equation as y = mx + b, where m is the slope and b is the y-intercept. It explains how to determine the points on a line by substituting values for x and how properties of linear functions include having a constant slope and unlimited domain and range. The document also covers solving systems of linear equations by finding the point where two lines intersect.
![Characteristics of Linear FunctionCharacteristics of Linear Function
CharacteristicCharacteristic Basic FnBasic Fn
DirectDirect
TransformedTransformed
PartialPartial
RuleRule y= 1xy= 1x y = ax+by = ax+b
a - #, b - y.i.a - #, b - y.i.
DomainDomain ]-∞,∞[]-∞,∞[ ]-∞,∞[]-∞,∞[
RangeRange ]-∞,∞[]-∞,∞[ ]-∞,∞[]-∞,∞[
ExtremeExtreme nonenone nonenone
Zero of fnZero of fn x = 0x = 0 -b/a-b/a
Sign: posSign: pos ]0,∞[]0,∞[ DependsDepends
Sign: negSign: neg ]-∞,0[]-∞,0[ DependsDepends](https://image.slidesharecdn.com/linearequations-160531032645/85/CST-504-Linear-Equations-8-320.jpg)
CST 504 Linear Equations
- 1. Linear EquationsLinear Equations Math CST 5Math CST 5
- 2. Function FormatFunction Format y = f(x) = ax + by = f(x) = ax + b Where y is a function of x, y is basedWhere y is a function of x, y is based on x.on x. ‘‘a’ is ROC/ slope =a’ is ROC/ slope = ΔyΔy == yy22-y-y11 Δx xΔx x22-x-x11 ‘‘b’ is the y intercept or initial value.b’ is the y intercept or initial value. E.g. y = 2x + 1E.g. y = 2x + 1 Slope is 2 and the y intercept is 1.Slope is 2 and the y intercept is 1.
- 3. Determining the Points of a LineDetermining the Points of a Line Given the equation: y = 2x + 7Given the equation: y = 2x + 7 Make a table:Make a table: Substitute values of x into y = 2x + 7Substitute values of x into y = 2x + 7 x y= 2x + 7 x y = 2x + 7 0 2(0) + 7 = 7 (0,7) 1 2(1) + 7 = 9 (1,9) 2 2(2) + 7 = 11 (2,11)
- 4. Determining the Points of a LineDetermining the Points of a Line Given the equation 2x – y = 7Given the equation 2x – y = 7 Make a table.Make a table. Substitute values in.Substitute values in. GraphGraph 2x - y = 7 2 (0) -(-7) 7 (0,-7) 2 (1) -(-5) 7 (1,-5) 2 (2) -(-3) 7 (2, -3)
- 6. PropertiesProperties Lines with the same slope, a, areLines with the same slope, a, are parallel.parallel. Lines with different slopes, a, mustLines with different slopes, a, must intersect somewhere.intersect somewhere. A positive slope goes up from left toA positive slope goes up from left to right.right. A negative slope goes down from left toA negative slope goes down from left to right.right. A line perpendicular (at 90°) to a lineA line perpendicular (at 90°) to a line with slope ‘a’ has a slope ‘-1/a’.with slope ‘a’ has a slope ‘-1/a’.
- 7. ExampleExample Given the points, (2,3) and (5,-6),Given the points, (2,3) and (5,-6), what is the equation of the line?what is the equation of the line? PagePage
- 8. Characteristics of Linear FunctionCharacteristics of Linear Function CharacteristicCharacteristic Basic FnBasic Fn DirectDirect TransformedTransformed PartialPartial RuleRule y= 1xy= 1x y = ax+by = ax+b a - #, b - y.i.a - #, b - y.i. DomainDomain ]-∞,∞[]-∞,∞[ ]-∞,∞[]-∞,∞[ RangeRange ]-∞,∞[]-∞,∞[ ]-∞,∞[]-∞,∞[ ExtremeExtreme nonenone nonenone Zero of fnZero of fn x = 0x = 0 -b/a-b/a Sign: posSign: pos ]0,∞[]0,∞[ DependsDepends Sign: negSign: neg ]-∞,0[]-∞,0[ DependsDepends
- 9. Solution of a SystemSolution of a System Solving a linear system meansSolving a linear system means finding the (x,y) where 2 linesfinding the (x,y) where 2 lines intersect.intersect. For the lines: y = -3x+6For the lines: y = -3x+6 And y = 5x -10And y = 5x -10 Make a table of valuesMake a table of values Graph the two lines on the sameGraph the two lines on the same graphgraph Find the (x,y) point of intersectionFind the (x,y) point of intersection
- 10. Solution of a SystemSolution of a System Solving a linear system meansSolving a linear system means finding the (x,y) where 2 linesfinding the (x,y) where 2 lines intersect.intersect. For the lines: y = -3x+6For the lines: y = -3x+6 And y = 5x -10And y = 5x -10 Make a table of valuesMake a table of values Graph the two lines on the sameGraph the two lines on the same graphgraph Find the (x,y) point of intersectionFind the (x,y) point of intersection