No, they are not the same.
If you made y the subject for each of them:
ax + by = d
by = -ax + d
y = -(a/b)x + (d/b)
which may not be the same as
y = mx + b
since b is already a fixed variable.
But I'm not sure if your question is just asking about whether ax + by = d can be expressed as linear form. If it was asking that, then the working above shows that it can be expressed in linear form (y = mx + b)
