SOLUTION: Write an equation of the line containing the given point and parallel to the givin line. (8,-4); 8x-5y=7

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Question 666801: Write an equation of the line containing the given point and parallel to the givin line. (8,-4); 8x-5y=7
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the given point (8,-4)
the given line 8x-5y=7
8x-7=5y
%288%2F5%29x-7%2F5=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 8%2F5 (its from the slope of y=%288%2F5%29%2Ax-7%2F5 which is also 8%2F5). Also since the unknown line goes through (8,-4), 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%2B4=%288%2F5%29%2A%28x-8%29 Plug in m=8%2F5, x%5B1%5D=8, and y%5B1%5D=-4



y%2B4=%288%2F5%29%2Ax-%288%2F5%29%288%29 Distribute 8%2F5



y%2B4=%288%2F5%29%2Ax-64%2F5 Multiply



y=%288%2F5%29%2Ax-64%2F5-4Subtract -4 from both sides to isolate y

y=%288%2F5%29%2Ax-64%2F5-20%2F5 Make into equivalent fractions with equal denominators



y=%288%2F5%29%2Ax-84%2F5 Combine the fractions



y=%288%2F5%29%2Ax-84%2F5 Reduce any fractions

So the equation of the line that is parallel to y=%288%2F5%29%2Ax-7%2F5 and goes through (8,-4) is y=%288%2F5%29%2Ax-84%2F5


So here are the graphs of the equations y=%288%2F5%29%2Ax-7%2F5 and y=%288%2F5%29%2Ax-84%2F5



graph of the given equation y=%288%2F5%29%2Ax-7%2F5 (red) and graph of the line y=%288%2F5%29%2Ax-84%2F5(green) that is parallel to the given graph and goes through (8,-4)