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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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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 
(both sides). You will get an equivalent equation
= 0. (3).
Now comparing the equation (3) with the equation ax + by - 5 = 0,
you can conclude that a = 
and b = 
.
Solved.
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comment from student: Hi! Thanks for helping me but can you please explain to me how 5x - 2y = c is perpendicular 2x - 5y + 5 = 0. Thank you!
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My response:
Let me first TO CORRECT your question. It should be
"can you please explain to me how 5x+2y=0 is perpendicular 2x-5y+5=0 ?"
5x + 2y = c has the slope 
.
2x - 5y + 5 = 0 has the slope 
The two slopes are reciprocal and have opposite signs !!
