SOLUTION: Write an equation for a line parallel to y = -2 x -1 and passing through the point (1,2) y= ?

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Question 990054: Write an equation for a line parallel to y = -2 x -1 and passing through the point (1,2)
y= ?

Answer by MathLover1(20849) 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-1 which is also -2). Also since the unknown line goes through (1,2), 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-2=-2%2A%28x-1%29 Plug in m=-2, x%5B1%5D=1, and y%5B1%5D=2



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



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



y=-2%2Ax%2B2%2B2Add 2 to both sides to isolate y

y=-2%2Ax%2B4 Combine like terms

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


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



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