Indicate the equation of the given line in standard form. the line containing the hypotenuse of right triangle abc where a(-5, 5), b(1, 1), and c(3, 4) are the vertices.

We have that
triangle ABC
where
A(-5, 5), B(1, 1), and C(3, 4) are the vertices

using a graph tool
see the attached figure

the hypotenuse is the segment AC

find the equation of the line AC
A(-5, 5) C(3, 4) 

step 1
find the slope m
m=(y2-y1)/(x2-x1)-----> m=(4-5)/(3+5)-----> m=-1/8

step 2
with C(3,4) and m=-1/8
find the equation of a line
y-y1=m*(x-x1)-----> y-4=(-1/8)*(x-3)----> y=(-1/8)*x+(3/8)+4
y=(-1/8)*x+(3/8)+4----> multiply by 8----> 8y=-x+3+32
8y=-x+35
the standard form is Ax+By=C
so
x+8y=35
A=1
B=8
C=35

the answer is
x+8y=35