Question 1129600
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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.<br>
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).<br>
Any line perpendicular to a line with equation Ax+By=C will have an equation of the form Bx-Ay=D.<br>
Use the appropriate forms of the equation and substitute the given (x,y) values to determine the constants.<br>
(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.<br>
ANSWER: x-5y=-28<br>
(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.<br>
ANSWER: -x+3y = -17, or (since most definitions of standard form require the coefficient of x to be positive) x-3y = 17<br>