<PRE><B>Question 792381</B>
Write the equation of a line parallel to the given line but passing through the given point.
y=-1/2x+1 (4,2)


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The slope of y=-1/2x+1 is m = -1/2 since the equation y=-1/2x+1  is in the form y = mx+b where m = -1/2 (slope) and b = 1 (y-intercept)


The slope of ANY line parallel to this one will also be -1/2, so m is still -1/2.


y = mx + b


y = (-1/2)x + b ... plug in the parallel slope


2 = (-1/2)(4) + b ... plug in the given point (4,2)


2 = (-1/2)(4/1) + b


2 = (-1*4)/(2*1) + b


2 = (-4)/(2) + b


2 = -2 + b


2 + 2 = b


4 = b


b = 4


Therefore, the slope is m = -1/2 and the y-intercept is b = 4


So y = mx+b turns into y = -1/2x + 4



The answer is {{{y = -expr(1/2)x + 4}}}


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Then write the equation of a line perpendicular to the given line but passing through the given point.
Y=-3x-6; (-1,5)


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y = -3x - 6 ----&gt; m = -3


Given slope: m = -3

Perpendicular slope: m = 1/3 (flip the fraction and flip the sign)



y = mx + b


y = (1/3)x + b ... plug in the perpendicular slope


5 = (1/3)(-1) + b ... plug in the given point (-1,5)


5 = (1/3)(-1/1) + b


5 = (1*(-1))/(3*1) + b


5 = -1/3 + b


5+1/3 = b


15/3+1/3 = b


16/3 = b


b = 16/3


Answer: {{{y = expr(1/3)x + 16/3}}}
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