Why is the point-slope form useful if you want to write the equation of a line through a point that is parallel to a given line.

The point slope form of a line is:

point (a,b)

slope: m

equation: (y - b) / (x - a) = m => y - b = m (x - a)

Where m is the slope of the parallel line.

You need to know that parallel lines have the same slope, so m is the slope of both lines.

These are equivalent forms of the equation searched and both are valid answers:

y - b = m (x - a)

y = m (x - a) + b