We want to find a scalar function

such that

.
So we need to have

Integrating both sides with respect to

gives

Differentiating with respect to

gives



So we find that

By the fundamental theorem of calculus, we then know the line integral depends only on the values of

at the endpoints of the path. Therefore
The fifth square root as in a^(1/2)^(1/2)^(1/2)^(1/2)^(1/2)
Well that is equal to a^((1/2)^5) or a^(1/32)
Since a=x^16 in this case and the rule (b^a)^c=b^(a*c) we have:
(x^16)^(1/32)
x^(16/32)
x^(1/2) or if you prefer
√x
Answer:
Slope intercept form; -4y = -3x + 9
Y-intercept; 9