SOLUTION: The line ax+by-5=0 passes through the point (-2,8) and is perpendicular to the line 2x-5y+5=0. Find the value of a and b.

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Question 1101807: The line ax+by-5=0 passes through the point (-2,8) and is perpendicular to the line 2x-5y+5=0. Find the value of a and b.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
5x%2B2y-5=0 must contain the point (-2,8).

Does the point satisfy the equation?
5%28-2%29%2B2%2A8-5=0
-10%2B16-5=0
-15%2B16=0
1=0-----FALSE!

Either I missed something or the problem description is incorrect.

Answer by ikleyn(52886) About Me  (Show Source):
You can put this solution on YOUR website!
.
The line perpendicular to the line 2x - 5y + 5 = 0 is the line of the form

5x + 2y = c,         (1)


where "c" is some constant which must be determined from the other condition,


         OR ANY OTHER EQUATION EQUIVALENT TO eq(1).



This other condition for "c" is "the line (1) passes through the point (-2,8)."


Therefore, we can determine "c" from the equation (1) by substituting x= -2  and  y= 8 into equation (1).  By doing so, you will get


5*(-2) + 2*8 = c = -10+16 = 6.


So, the equation of the line (1) is 


5x + 2y = 6,   or


5x + 2y - 6 = 0.      (2)


Now multiply eq(2) by 5%2F6 (both sides).  You will get an equivalent equation 


%2825%2F6%29%2Ax+%2B+%2810%2F6%29y+-+5 = 0.   (3).


Now comparing the equation (3) with the equation ax + by - 5 = 0,  

you can conclude that  a = 25%2F6   and  b = 10%2F6.

Solved.