Equations for LinesDate: 5/29/96 at 16:19:0 From: CHAD E MILBURN Subject: Algebra Wordproblem Dear Dr. Math, My brother is taking a correspondence course in Algebra 2 and there are a couple of word problems we can't figure out. I have tried helping him but word problems I cannot do! 1. Write an equation, in standard form, of the line containing the point P(1,-3) that is parallel to the line whose equation is 2x-y=3. 2. Write an equation, in standard form, of the line containing Q(-5,4) that is perpendicular to the line whose equation is 3x-2y=8. Date: 5/30/96 at 14:19:6 From: Doctor Darren Subject: Re: Algebra Wordproblem 1. We know that this line can also be written in the form y=2x-3, so it and all lines parallel to it have slope = 2. We now have a point on our line and its slope, so we can write the line in point-slope form as: (y-(-3)) = 2(x-1) y+3 = 2x-2 2x-y = 5 2. The line 3x-2y=8 has slope equal to 3/2. We know that if two lines are perpendicular then their slopes are negative reciprocals of each other (i.e. if a line has slope m, all lines perpendicular to it have slope -1/m). So the slope of the line that we want is -2/3. As in the previous problem, we now have the slope of the line and a point on the line. Therefore, the line can be written in point-slope form as: y-4 = (-2/3)(x-(-5)) y-4 = (-2/3)x - 10/3 3y-12 = -2x-10 3y+2x = 2 I hope this helps! -Doctor Darren, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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