SOLUTION: Find an equation of the line through the point (3 , 5) that is perpendicular to the line 2X+5Y=4

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Question 1197785: Find an equation of the line through the point (3 , 5) that is perpendicular to the line 2X+5Y=4
Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi  
Find an equation of the line through the point  (3 , 5) 
that is perpendicular to the line 2X+5Y=4 0r  green
New Line(Blue): m = 5/2, goes thru P(3,5)
 y - 5 = (5/2)(x  - 3)
     y = (5/2)x -5/2 (Note: slants right)
or 2y - 5x = -5


Wish You the Best in your Studies.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


For solving using elementary methods, you can use the method shown by the other tutor: determine the slope of the graph of the given equation, find the slope of a line perpendicular to the given line, and use that slope and the given point to find the equation.

You can solve the problem with much less work using this fact:
Given a line with equation in the form Ax+By=C, the equation of any line PARALLEL to the given line is also of the form Ax+By=D, and the equation of any line PERPENDICULAR to the given line has an equation of the form Bx-Ay=E.

So any line perpendicular to the given line 2x+5y=4 has an equation of the form 5x-2y=C.

To find the one that passes through (3,5), substitute those values in the equation to determine the constant C:

5(3)-2(5) = 15-10 = 5

ANSWER: 5x-2y = 5
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