<PRE><B>Question 285990</B>
 -4x + 5y = 17
5y = 4x + 17
y = (4/5)x + 17/5
.
therefore, the slope of this line is 4/5.
which means the slope of a perpendicular line is -5/4.
.
We want this line with slope = -5/4 to go through the point (-2,5).
y = mx+b
5 = (-5/4)(-2) + b
5 = 10/4 + b
5 - 10/4 = b
5 - 2.5 = b
b = 2.5
.
y = -5/4x + 2.5
.
You can check with a graph.  The red line is y = (4/5)x + 17/5. The green line is 
y = -5/4x + 2.5
.
{{{
drawing(500,500,-10,10,-10,10,
blue(circle(-2,5,.2)),
graph(500,500,-10,10,-10,10,4/5*x + 17/5,-5/4*x + 2.5)
)}}}
.</PRE>