implicit differentiation?

Question

Consider the differential equation dy/dx = x-1

1. Sketch a slope field for the given differential equation at the twelve indicated points.
2. Sketch the solution curve through the point (1, 0).
3.  Find y = f(x) by solving the differential equation dy/dx = x-1 with the initial condition f(1) = 0

Answer 1

I have already solved this one for you as well....

Please only post one copy of the problem.

Thank you

dy/dx = x-1

dy = (x-1) dx <-- separation of variables

y =(1/2) x^2 - x + c <--- integrates both sides

f(1) = 0 ---> 0 = (1/2)*1^2 - 1 + c

0 = 1/2 - 1 + c

0 = c - 1/2

c = 1/2

y =1/2* x^2 - x + 1/2