Question 1203422
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Answer: <font color=red size=4>y = (-5/2)x + 5</font>



Explanation


2x - 5y = -10 is of the form Ax+By = C, where,
A = 2
B = -5
C = -10


Anything perpendicular to Ax+By = C is of the form Bx-Ay = D
We swap the positions of A and B, then negate one of them. 


So all equations perpendicular to 2x-5y = -10 will look like -5x-2y = D.
We can multiply both sides by -1 to get rid of both negative signs on the left hand side, and we end up with 5x+2y = D.


To determine D, we plug in the coordinates (4,-5)
D = 5x+2y
D = 5*4+2(-5)
D = 20 - 10
D = 10


Therefore, the standard form equation perpendicular to the original, and that passes through (4,-5) is 5x+2y = 10 


Let's solve that for y to get it into slope-intercept form.
5x+2y = 10 
2y = 10-5x 
2y = -5x+10 
y = (-5x+10)/2 
y = (-5x)/2+10/2 
<font color=red size=4>y = (-5/2)x+5 </font> which is the final answer.


This is in the form y = mx+b
m = -5/2 = perpendicular slope
b = 5 = y intercept
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