SOLUTION: a line parallel to the graph 2x + y = 5 thru (2,-3)

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Question 1008967: a line parallel to the graph 2x + y = 5 thru (2,-3)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
2x+%2B+y+=+5
y+=+-2x%2B5
(2,-3)

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%2B5 which is also -2). Also since the unknown line goes through (2,-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-2%29 Plug in m=-2, x%5B1%5D=2, and y%5B1%5D=-3



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



y%2B3=-2%2Ax%2B4 Multiply



y=-2%2Ax%2B4-3Subtract -3 from both sides to isolate y

y=-2%2Ax%2B1 Combine like terms

So the equation of the line that is parallel to y=-2%2Ax%2B5 and goes through (2,-3) is y=-2%2Ax%2B1


So here are the graphs of the equations y=-2%2Ax%2B5 and y=-2%2Ax%2B1



graph of the given equation y=-2%2Ax%2B5 (red) and graph of the line y=-2%2Ax%2B1(green) that is parallel to the given graph and goes through (2,-3)