Question 1110417: Find the equation of the line which passes through the point (-3,5) and is perpendicular to the line 4x+3y=6. Express your answer in slope intercept form.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! the line which passes through the point ( , ) and is  to the line  or  is:
| 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  , you can find the perpendicular slope by this formula:
 where  is the perpendicular slope
 So plug in the given slope to find the perpendicular slope
 When you divide fractions, you multiply the first fraction (which is really  ) by the reciprocal of the second
 Multiply the fractions.
So the perpendicular slope is 
So now we know the slope of the unknown line is (its the negative reciprocal of from the line  ).
Also since the unknown line goes through (-3,5), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
 where m is the slope and ( , ) is the given point
 Plug in  ,  , and 
 Distribute
 Multiply
 Add to both sides to isolate y
 Make into equivalent fractions with equal denominators
 Combine the fractions
Reduce any fractions
So the equation of the line that is perpendicular to and goes through (,) is
So here are the graphs of the equations and
 graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)
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Answer by ikleyn(52781)  (Show Source):
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