How is the final answer resulting from a point-slope formula different than the one resulting from the slope-intercept formula?

Question

Do you leave the point-slope form as it is or do you need to simplify it to match the slope-intercept form?

Answer 1

Nancy,

 

The solution (or answer) is the line itself, and it is identical in all cases.  Only its appearance or representation of that solution is slightly different:

 

y = mx + b  is the slope-intercept form of that line

y = m(x - h) + k, or (y - k) = m (x - h)  is the point-slope form of that line.

ax + by = c  is the standard form that isolates the constant on the right-hand side of the equation.

 

Unless the statement of the problem calls out a required form to put the solution into, I would go with the slope-intercept form because it's easy to read, already reduced and familiar from Geometry.  The other two forms are more like starting rather than ending forms because you either have multiple constants or a coefficient on y so some work "should" follow.