Writing equations of lines parallel and perpendicular to a given line through a point

Question

Consider the line y=5/4x-9

Find the equation of the line that is parallel to this line and passes through the point (5,5). Find the equation of the line that is perpendicular to this line and passes through the point (5,5).

Answer 1

y = 5x/4 - 9 has slope = 5/4

any parallel line has the same slope

y-5 = (5/4)(x-5) = 5x/4 -25/4

y= 5x/4 -25/4 +20/4

y = (5/4)x - 5/4

is in y=mx+b form where m= slope = 5/4

and b = y intercept = -5/4