The vertices of ghk above have coordinates g(-3,4), h (1.-3), and k(2,7). the equation of the altitude to hk is

We know that
the equation of the altitude to hk passes through point g and is perpendicular to segment hk

step 1
find the slope segment hk
h (1.-3)  k(2,7)
slope m=(y2-y1)/(x2-x1)----> m=(7+3)/(2-1)----> m=10

if two lines are perpendicular
so
m1*m2=-1

the altitude to hk has a slope
m2=-1/10

step 2
with m=-1/10 and point g(-3,4) find the equation of the line
y-y1=m*(x-x1)-----> y-4=(-1/10)*(x+3)---> multiply by 10
10y-40=-x-3----> 10y+x=37-----> equation of the altitude

the answer is 
10y+x=37

see the attached figure