SOLUTION: I need help! please help! write an equation of the line containing the given point and parallel to the given linr. express your answer in the form y=mx+b. (5,9:x+2y=7 number 2 ques

Question 172080: I need help! please help! write an equation of the line containing the given point and parallel to the given linr. express your answer in the form y=mx+b. (5,9:x+2y=7 number 2 question. write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b. (-9,7);5x=7y+9 The equation of the line is y=?, and the third question. write an equation of the line containing the given point and perpendicular to the given line. (6,7):2x+y=4 The equation of the line is y=?.
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
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.
:
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
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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--->

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