SOLUTION: please help me with this word problem: find an equation of the line containing the point (-1,3)and perpendicular to the line x + 2y = -6. Thanks in advance

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Question 905819: please help me with this word problem: find an equation of the line containing the point (-1,3)and perpendicular to the line x + 2y = -6. Thanks in advance
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
an equation of the line containing the point (-1,3)and perpendicular to the line x+%2B+2y+=+-6:
x+%2B+2y+=+-6...solve for y
2y+=-x-6
y+=+-%281%2F2%29x-6%2F2
y+=+-%281%2F2%29x-3

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%2F2, 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%28-1%2F2%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%282%2F-1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



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


So the perpendicular slope is 2



So now we know the slope of the unknown line is 2 (its the negative reciprocal of -1%2F2 from the line y=%28-1%2F2%29%2Ax-3). Also since the unknown line goes through (-1,3), 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-3=2%2A%28x%2B1%29 Plug in m=2, x%5B1%5D=-1, and y%5B1%5D=3



y-3=2%2Ax-%282%29%28-1%29 Distribute 2



y-3=2%2Ax%2B2 Multiply



y=2%2Ax%2B2%2B3Add 3 to both sides to isolate y

y=2%2Ax%2B5 Combine like terms

So the equation of the line that is perpendicular to y=%28-1%2F2%29%2Ax-3 and goes through (-1,3) is y=2%2Ax%2B5


So here are the graphs of the equations y=%28-1%2F2%29%2Ax-3 and y=2%2Ax%2B5




graph of the given equation y=%28-1%2F2%29%2Ax-3 (red) and graph of the line y=2%2Ax%2B5(green) that is perpendicular to the given graph and goes through (-1,3)