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Question 1129600: Write the equation of the line that satisfies the given conditions. Express the final equation in standard form.
Contains the point (-3, 5) and is PARALLEL to the line x − 5y = 6
Contains the point (-4, 7) and is PERPENDICULAR to the line 3x − y = 4
I took this question from the example questions in the textbook to prepare myself for an exam that is coming up soon. I've been stuck on these two problems for around an hour so any and all help is greatly appreciated. Thank you!
Found 4 solutions by stanbon, greenestamps, josmiceli, ikleyn:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write the equation of the line that satisfies the given conditions. Express the final equation in standard form.
Contains the point (-3, 5) and is PARALLEL to the line x − 5y = 6
Solve the equation for "y"::
5y = x-6
y = (1/5)x-(6/5)
The slope is 1/5
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Equation of line with slope = 1/5 passing thru point (-3,5)
(y-5)/(x+3) = 1/5
x+3 = 5y-25
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Standard Form:: x-5y = -28
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Contains the point (-4, 7) and is PERPENDICULAR to the line 3x − y = 4
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Find the slope of the given equation::
y = 3x-4
slope = 3
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Equation we want must have slope = -1/3 and must pass thru (-4,7)
y-7 = (-1/3)(x+4)
Find the standard form::
x+4 = -3(y-7)
x+4 = -3y+21
Ans:: x + 3y = 17
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Cheers,
Stan H.
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Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Since the problem asks for the equations in standard form, and the given equations are in standard form, there is no need (it is a waste of time) to convert the given equations to slope-intercept form to find their slopes.
Any line parallel to a line with equation Ax+By=C will have an equation of the form Ax+By=D (where D is some different constant).
Any line perpendicular to a line with equation Ax+By=C will have an equation of the form Bx-Ay=D.
Use the appropriate forms of the equation and substitute the given (x,y) values to determine the constants.
(a) parallel to x-5y=6 through (-3,5). A=1, B=-5; the constant is Ax+By = 1(-3)+-5(5) = -3-25 = -28.
ANSWER: x-5y=-28
(b) perpendicular to 3x-y=4 through (-4,7). A=3, B=-1 the constant is Bx-Ay = -1(-4)-3(7) = 4-21 = -17.
ANSWER: -x+3y = -17, or (since most definitions of standard form require the coefficient of x to be positive) x-3y = 17
Answer by josmiceli(19441)  (Show Source):
Answer by ikleyn(52781)  (Show Source):
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