SOLUTION: Find the equation of the line that passes through the point (1, -3) and is parallel to the line y = -2x + 4

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Question 87015: Find the equation of the line that passes through the point (1, -3) and is parallel to the line y = -2x + 4
Answer by jim_thompson5910(35256) 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 -2 (its from the slope of y=-2%2Ax%2B4 which is also -2). Also since the unknown line goes through (1,-3), 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%2B3=-2%2A%28x-1%29 Plug in m=-2, x%5B1%5D=1, and y%5B1%5D=-3



y%2B3=-2%2Ax%2B%282%29%281%29 Distribute -2



y%2B3=-2%2Ax%2B2 Multiply



y=-2%2Ax%2B2-3Subtract -3 from both sides to isolate y

y=-2%2Ax-1 Combine like terms

So the equation of the line that is parallel to y=-2%2Ax%2B4 and goes through (1,-3) is y=-2%2Ax-1


So here are the graphs of the equations y=-2%2Ax%2B4 and y=-2%2Ax-1



graph of the given equation y=-2%2Ax%2B4 (red) and graph of the line y=-2%2Ax-1(green) that is parallel to the given graph and goes through (1,-3)