SOLUTION: How would I write the equation of the line which has y-intercept (0,5) and is perpendicular to the line with equation y = -3x + 1?

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Question 120521: How would I write the equation of the line which has y-intercept (0,5) and is perpendicular to the line with equation y = -3x + 1?
Found 2 solutions by jim_thompson5910, tutor_paul:
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


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of -3, 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%28-3%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-3%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%2F3 Multiply the fractions.


So the perpendicular slope is 1%2F3



So now we know the slope of the unknown line is 1%2F3 (its the negative reciprocal of -3 from the line y=-3%2Ax%2B1). Also since the unknown line goes through (0,5), 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-5=%281%2F3%29%2A%28x-0%29 Plug in m=1%2F3, x%5B1%5D=0, and y%5B1%5D=5



y-5=%281%2F3%29%2Ax-%281%2F3%29%280%29 Distribute 1%2F3



y-5=%281%2F3%29%2Ax-0%2F3 Multiply



y=%281%2F3%29%2Ax-0%2F3%2B5Add 5 to both sides to isolate y

y=%281%2F3%29%2Ax-0%2F3%2B15%2F3 Make into equivalent fractions with equal denominators



y=%281%2F3%29%2Ax%2B15%2F3 Combine the fractions



y=%281%2F3%29%2Ax%2B5 Reduce any fractions

So the equation of the line that is perpendicular to y=-3%2Ax%2B1 and goes through (0,5) is y=%281%2F3%29%2Ax%2B5


So here are the graphs of the equations y=-3%2Ax%2B1 and y=%281%2F3%29%2Ax%2B5




graph of the given equation y=-3%2Ax%2B1 (red) and graph of the line y=%281%2F3%29%2Ax%2B5(green) that is perpendicular to the given graph and goes through (0,5)

Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that lines which are perpendicular to each other have slopes which are negative reciprocals of each other. So the slope of the line they are asking you for is the negative reciprocal of -3, which is 1/3. They are giving you the Y-intercept, so now it is easy to write out the equation of the line in slope/intercept form as follows:
highlight%28y=x%2F3%2B5%29
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Good Luck,
tutor_paul@yahoo.com