SOLUTION: line l goes through (4,-2) and is parallel to 4x+2y=5

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Question 417438: line l goes through (4,-2) and is parallel to 4x+2y=5
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

line l goes through (4,-2) and is parallel to 4x%2B2y=5
2y=-4x%2B5
y=-4x%2F2%2B5%2F2
y=-2x%2B2.5

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%2B2.5 which is also -2). Also since the unknown line goes through (4,-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%2B2=-2%2A%28x-4%29 Plug in m=-2, x%5B1%5D=4, and y%5B1%5D=-2



y%2B2=-2%2Ax%2B%282%29%284%29 Distribute -2



y%2B2=-2%2Ax%2B8 Multiply



y=-2%2Ax%2B8-2Subtract -2 from both sides to isolate y

y=-2%2Ax%2B6 Combine like terms

So the equation of the line that is parallel to y=-2%2Ax%2B2.5 and goes through (4,-2) is y=-2%2Ax%2B6


So here are the graphs of the equations y=-2%2Ax%2B2.5 and y=-2%2Ax%2B6



graph of the given equation y=-2%2Ax%2B2.5 (red) and graph of the line y=-2%2Ax%2B6(green) that is parallel to the given graph and goes through (4,-2)