SOLUTION: find the equation of the line that contains the point (3,-6) and parallel to y=-3x-5

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Question 462489: find the equation of the line that contains the point (3,-6) and parallel to y=-3x-5
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
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 -3 (its from the slope of y=-3%2Ax-5 which is also -3). Also since the unknown line goes through (3,-6), 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%2B6=-3%2A%28x-3%29 Plug in m=-3, x%5B1%5D=3, and y%5B1%5D=-6



y%2B6=-3%2Ax%2B%283%29%283%29 Distribute -3



y%2B6=-3%2Ax%2B9 Multiply



y=-3%2Ax%2B9-6Subtract -6 from both sides to isolate y

y=-3%2Ax%2B3 Combine like terms

So the equation of the line that is parallel to y=-3%2Ax-5 and goes through (3,-6) is y=-3%2Ax%2B3


So here are the graphs of the equations y=-3%2Ax-5 and y=-3%2Ax%2B3



graph of the given equation y=-3%2Ax-5 (red) and graph of the line y=-3%2Ax%2B3(green) that is parallel to the given graph and goes through (3,-6)