Begin with the point-slope form in Problem 58 and derive the two-point form. If the line passes through \(\left(x_{1}, y_{1}ight)\) and \(\left(x_{2}, y_{2}ight)\), then

\[y-y_{1}=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}ight)\left(x-x_{1}ight)\]

Data from problem 58

Show that the equation of a line passing through \((h, k)\) with slope \(m\) is

\[y-k=m(x-h)\]

This is called the point-slope form.