SOLUTION: Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. Contains the point (-1, 7) and is parallel to the line x −

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Question 457363: Write the equation of the line that satisfies the given conditions. Express the final equation in standard form.
Contains the point (-1, 7) and is parallel to the line x − 7y = 6

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the point (-1, 7) and is parallel to the line x-7y+=+6+
x-6+=+7y+
%281%2F7%29x-6%2F7+=+y+

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 1%2F7 (its from the slope of y=%281%2F7%29%2Ax-6%2F7 which is also 1%2F7). Also since the unknown line goes through (-1,7), 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-7=%281%2F7%29%2A%28x%2B1%29 Plug in m=1%2F7, x%5B1%5D=-1, and y%5B1%5D=7



y-7=%281%2F7%29%2Ax-%281%2F7%29%28-1%29 Distribute 1%2F7



y-7=%281%2F7%29%2Ax%2B1%2F7 Multiply



y=%281%2F7%29%2Ax%2B1%2F7%2B7Add 7 to both sides to isolate y

y=%281%2F7%29%2Ax%2B1%2F7%2B49%2F7 Make into equivalent fractions with equal denominators



y=%281%2F7%29%2Ax%2B50%2F7 Combine the fractions



y=%281%2F7%29%2Ax%2B50%2F7 Reduce any fractions

So the equation of the line that is parallel to y=%281%2F7%29%2Ax-6%2F7 and goes through (-1,7) is y=%281%2F7%29%2Ax%2B50%2F7


So here are the graphs of the equations y=%281%2F7%29%2Ax-6%2F7 and y=%281%2F7%29%2Ax%2B50%2F7



graph of the given equation y=%281%2F7%29%2Ax-6%2F7 (red) and graph of the line y=%281%2F7%29%2Ax%2B50%2F7(green) that is parallel to the given graph and goes through (-1,7)