section 1_10

section 1_10 - Math 1650 Lecture Notes §1.10 Jason Snyder...

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Unformatted text preview: Math 1650 Lecture Notes §1.10 Jason Snyder, PhD. Lines Page 1 of 9 § 1.10: Lines The Slope of a Line For a line, we will define the run to be the distance we move to the right and the rise to be the corresponding distance that the rises (or falls). The slope of the line is the ratio of rise to run: ????¡ = ¢?¡ ¢£? The following pictures illustrate some applications of slope. If a line lies in the xy-plane, then the rise is the change in the y-coordinate while the run is the change in the x-coordinate. Math 1650 Lecture Notes §1.10 Jason Snyder, PhD. Lines Page 2 of 9 This gives the following definition of slope. Example 1 Finding the Slope of a Line through Two Points Find the slope of the line that passes through the points (2,1) and (8,8). Equations of Lines Now let’s find an equation of the line passing through a given point A(x 1 ,y 1 ) and has slope m . A point B(x,y), with x x 1 , lies on this line if and only if the slope of the line through A and B is equal to m , that is ? − ? 1 ? − ? 1 = ¡ . By multiplying both sides by x-x 1 we obtain ¡ = ?¢£ ??¤ = ? 2 − ? 1 ? 2 − ? 1 . Slope of a line The slope of a non-vertical line that passes through the points A(x 1 ,y 1 ) and B(x 2 ,y 2 ) is given by The slope of a vertical line is undefined. ? − ? 1 = ¡ ? − ? 1 ¥ . Point-Slope Form of the Equation of a Line An equation of the line that passes through the point (x 1 ,y 1 ) and has slope m is Math 1650 Lecture Notes §1.10 Jason Snyder, PhD. Jason Snyder, PhD....
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This note was uploaded on 10/07/2009 for the course MATH 150 taught by Professor Unknown during the Spring '06 term at Ohio State.

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section 1_10 - Math 1650 Lecture Notes §1.10 Jason Snyder...

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