SOLUTION: What is the equation of the line passing through (0, 2) and perpendicular to the line y = 4x – 3 in slope-intercept form?

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Question 636324: What is the equation of the line passing through (0, 2) and perpendicular to the line y = 4x – 3 in slope-intercept form?
Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20849) 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 4, 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%284%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F4%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%2F4 Multiply the fractions.


So the perpendicular slope is -1%2F4



So now we know the slope of the unknown line is -1%2F4 (its the negative reciprocal of 4 from the line y=4%2Ax-3). 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=%28-1%2F4%29%2A%28x-0%29 Plug in m=-1%2F4, x%5B1%5D=0, and y%5B1%5D=2



y-2=%28-1%2F4%29%2Ax%2B%281%2F4%29%280%29 Distribute -1%2F4



y-2=%28-1%2F4%29%2Ax-0%2F4 Multiply



y=%28-1%2F4%29%2Ax-0%2F4%2B2Add 2 to both sides to isolate y

y=%28-1%2F4%29%2Ax-0%2F4%2B8%2F4 Make into equivalent fractions with equal denominators



y=%28-1%2F4%29%2Ax%2B8%2F4 Combine the fractions



y=%28-1%2F4%29%2Ax%2B2 Reduce any fractions

So the equation of the line that is perpendicular to y=4%2Ax-3 and goes through (0,2) is y=%28-1%2F4%29%2Ax%2B2


So here are the graphs of the equations y=4%2Ax-3 and y=%28-1%2F4%29%2Ax%2B2




graph of the given equation y=4%2Ax-3 (red) and graph of the line y=%28-1%2F4%29%2Ax%2B2(green) that is perpendicular to the given graph and goes through (0,2)

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.

line passing through (0, 2) and perpendicular to the line y = 4x – 3, m = 4

New Line:  m+=+-1%2F4 Note: negative reciprocal of 4

 y = (-1/4)x + b

 2 = (-1/4)·0  + b   |Using ordered pair (x,y): (0,2)  to solve for b

 2 = b

 y = (-1/4)x + 2