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MTH 070 Elementary Algebra
Chapter 3 Linear Equations, Slope, Inequalities, and Introduction to Functions Section 3.4 Determining the Equation of a Line, Parallel Lines, and Perpendicular Lines Copyright © 2010 by Ron Wallace, all rights reserved.
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Linear Equations in Two Variables – Where we’ve been…
Two Forms Standard form: Ax + By = C x-intercept: (C/A,0) y-intercept: (0,C/B) Slope-Intercept from: y = mx + b slope: y-intercept: (0,b) Graph Two points need Picture of ALL ordered pairs/solutions
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Finding the Equation Often we know information about a line and need to determine its equation. Possible sufficient information 5 options ……….?
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Finding the Equation Often we know information about a line and need to determine its equation. Possible sufficient information Two Points (most common in applications) A Point and the Slope The y-intercept & the Slope Both intercepts (not origin) Graph
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Finding the Equation Two Points (most common in applications)
Calculate the slope Use the slope and either point to determine the equation (next option) Example: (2,3) & (–5,7)
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Finding the Equation A Point and the Slope Example: (2,3) & m = –4/7
Use the slope formula with (x,y) as one point and the given point as the other point. Example: (2,3) & m = –4/7
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Most general method – works in all situations!
Finding the Equation Point-Slope Forms Most general method – works in all situations!
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Finding the Equation The y-intercept & the Slope
Use the slope-intercept form y = mx + b m = slope b = y-intercept Example: (0,9) & m = 3
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Finding the Equation Both intercepts (not origin) Method 1
Special case of two points: (a,0) & (0,b) Method 1 Calculate m = –b/a & use y = mx + b Example: (2,0) & (0,–5)
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Finding the Equation Both intercepts (not origin) Method 1 Method 2
Special case of two points: (a,0) & (0,b) Method 1 Calculate m = –b/a & use y = mx + b Method 2 Write intercepts as fractions with the same numerator: (C/A,0) & (0, C/B) Use standard form: Ax + By = C Example: (2,0) & (0,–5)
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Finding the Equation Graph Example:
By observation, determine two points or one point and the slope (rise/run) Note: If possible, use the y-intercept Example:
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Finding the Equation Horizontal Lines Example:
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Finding the Equation Vertical Lines Example:
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Finding the Equation Parallel Lines Examples
What is true about parallel lines? Same slope Examples Find the equation through (0,3) that is parallel to y = 2x + 5 Find the equation through (2,3) that is parallel to y = 2x + 5
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Finding the Equation Perpendicular Lines
What is true about perpendicular lines? Slopes have opposite signs m2 = –1/m1
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Slopes of Perpendicular Lines
90 c Slope of Red Line = b Slope of Blue Line = c
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Finding the Equation Perpendicular Lines Examples
What is true about perpendicular lines? m2 = –1/m1 Examples Find the equation through (0,3) that is perpendicular to y = 2x + 5 Find the equation through (2,3) that is perpendicular to y = 2x + 5
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