SOLUTION: how do you write an equation of the line containing the given point and parallel to the given line? (3,7);x+2y=6 (2,-1);5x-7y=8

Question 65791This question is from textbook Algebra and Trigonometry
: how do you write an equation of the line containing the given point and parallel to the given line?
(3,7);x+2y=6
(2,-1);5x-7y=8 This question is from textbook Algebra and Trigonometry

Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
FIRST WE NEED TO FIND THE SLOPE OF THE LINE THUS
X+2Y=6
2Y=-X+6
Y=-X/2+6/2
Y=-X/2+3 THUS THE SLOPE OF THIS LINE IS -1/2.
SO THE LINE PARRALLEL TO THIS LINE MUST ALSO HAVE A SLOPE OF -1/2.
TO FIND THE EQUATION FOR THIS LINE WE SUBSTITUTE 3 FOR X & 7 FOR Y INTHE LINE FORMULA Y=mX+b THUS:
7=-3/2+b
b=7+3/2
b=7+1.5
b=8.5 THUS THE FORMULA FOR THE LINE WITH A SLOPE OF -1/2 AND PASSING THROUGH THE POINT (3,7) IS:
Y=-X/2+8.5
----------------------------------------------------------------------
5X-7Y=8 AGAIN FIND THE SLOPE
-7Y=-5X+8
Y=-5X/-7+8/-7
Y=-5/7X-8/7 THIS LINE HAS A SLOPE OF -5/7.
AGAIN SUBSTITUTE THE X & Y VALUES OF THE POINT AND FIND THE Y INTYERCEPT OF THIS LINE
Y=mX+b
-1=-5/7*2+b
b=-10/7+1
b=-(10+7)/7
b=-17/7 THUS THE EQUATION FOR THIS LINE IS
Y=-5/7X-17/7

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