SOLUTION: What is the equation for a line, in slope form, that is perpendicular to -x+y=4 that passes through (0,2)?

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Question 755172: What is the equation for a line, in slope form, that is perpendicular to -x+y=4 that passes through (0,2)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

perpendicular to -x%2By=4 that passes through (0,2)
in slope form you have y=x%2B4
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 1, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%281%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-1%2F1 Multiply the fractions.


So the perpendicular slope is -1



So now we know the slope of the unknown line is -1 (its the negative reciprocal of 1 from the line y=1%2Ax%2B4). Also since the unknown line goes through (0,2), 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=-1%2A%28x-0%29 Plug in m=-1, x%5B1%5D=0, and y%5B1%5D=2



y-2=-1%2Ax%2B%281%29%280%29 Distribute -1



y-2=-1%2Ax-0 Multiply



y=-1%2Ax-0%2B2Add 2 to both sides to isolate y

y=-1%2Ax%2B2 Combine like terms

So the equation of the line that is perpendicular to y=1%2Ax%2B4 and goes through (0,2) is y=-1%2Ax%2B2


So here are the graphs of the equations y=1%2Ax%2B4 and y=-1%2Ax%2B2




graph of the given equation y=1%2Ax%2B4 (red) and graph of the line y=-1%2Ax%2B2(green) that is perpendicular to the given graph and goes through (0,2)