SOLUTION: (4,-2), parallel to -5x+7y=69

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Question 974201: (4,-2), parallel to -5x+7y=69
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
(4,-2), parallel to -5x%2B7y=69=>y=%285%2F7%29x%2B69%2F7

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 5%2F7 (its from the slope of y=%285%2F7%29%2Ax%2B69%2F7 which is also 5%2F7). Also since the unknown line goes through (4,-2), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B2=%285%2F7%29%2A%28x-4%29 Plug in m=5%2F7, x%5B1%5D=4, and y%5B1%5D=-2



y%2B2=%285%2F7%29%2Ax-%285%2F7%29%284%29 Distribute 5%2F7



y%2B2=%285%2F7%29%2Ax-20%2F7 Multiply



y=%285%2F7%29%2Ax-20%2F7-2Subtract -2 from both sides to isolate y

y=%285%2F7%29%2Ax-20%2F7-14%2F7 Make into equivalent fractions with equal denominators



y=%285%2F7%29%2Ax-34%2F7 Combine the fractions



y=%285%2F7%29%2Ax-34%2F7 Reduce any fractions

So the equation of the line that is parallel to y=%285%2F7%29%2Ax%2B69%2F7 and goes through (4,-2) is y=%285%2F7%29%2Ax-34%2F7


So here are the graphs of the equations y=%285%2F7%29%2Ax%2B69%2F7 and y=%285%2F7%29%2Ax-34%2F7



graph of the given equation y=%285%2F7%29%2Ax%2B69%2F7 (red) and graph of the line y=%285%2F7%29%2Ax-34%2F7(green) that is parallel to the given graph and goes through (4,-2)