SOLUTION: determine the equation of a line using the given information: Parallel to the line y=-2x+3 containing the point (-2,-1) please show the steps so i may understand how you got the an

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Question 94113: determine the equation of a line using the given information: Parallel to the line y=-2x+3 containing the point (-2,-1) please show the steps so i may understand how you got the answer
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%2B3 which is also -2). Also since the unknown line goes through (-2,-1), 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%2B1=-2%2A%28x%2B2%29 Plug in m=-2, x%5B1%5D=-2, and y%5B1%5D=-1



y%2B1=-2%2Ax%2B%282%29%28-2%29 Distribute -2



y%2B1=-2%2Ax-4 Multiply



y=-2%2Ax-4-1Subtract -1 from both sides to isolate y

y=-2%2Ax-5 Combine like terms

So the equation of the line that is parallel to y=-2%2Ax%2B3 and goes through (-2,-1) is y=-2%2Ax-5


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



graph of the given equation y=-2%2Ax%2B3 (red) and graph of the line y=-2%2Ax-5(green) that is parallel to the given graph and goes through (-2,-1)