Question 172080
in all 3 cases you must determine the slope of the given equation.  Remember in the form y=mx+b that the slope is m and the y intercept is b.  since 1 and 2 are similar I will do # 1 and 3 and you can do number 2.
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1.) In problems 1 and 2 the slopes must be equal to be parallel..First we have to re write the equation into y=mx+b format to get the slope. x+2y=7--->subtract x from both sides--->2y=-x+7-->divide by 2 on both sides--->
y=(-1/2)x+7/2.....so the slope is -1/2.  Now we have the slope of the line parallel and the given point (5,9).  We must use the point slope formula which is y-k=m(x-h) where m is the slope and (h,k) is a point on the line.  
y-9=(-1/2)(x-5)....we need to distribute the right side and then put this in y=mx+b format.  y-9=-1/2x+5/2--->add 9 to both sides. y=(-1/2)x+23/2{{{highlight(y=(-1/2)x+23/2)}}}
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3.)The only difference in #3 and problems 1 and 2 is this is looking for a line perpendicular meaning instead of the slope being equal, a line perpendicular to another has a slope which is the negative inverse.  so again first we must find the slope of given equation. we do this by putting it in y=mx+b format.
2x+y=4 point (6,7)..  subtract 2x from both sides y=-2x+4....the slope of this line is -2..therefore any line perpendicular will have a slope 1/2 which is the negative inverse of -2.  we now have the slope and a point....using the point slope formula.  y-7=(1/2)(x-6)....distribute and write in y=mx+b format.
y-7=1/2x-3....add 7 to each side--->{{{highlight(y=(1/2)x+4)}}}