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

Question

Consider the line y=-3x+9.

Find the equation of the line that is parallel to this line and passes through the point (7, -6).

Answer 1

-6 = -3(7) + b

b = -6 +21 = 15

y = -3x + 15 is the parallel line through the point (7,-6)

parallel lines have the same slope

the slope = the coefficient of the x term when the equation is solved for y. the slope = m = -3

y=mx + b is the standard equation in slope intercept form

y=-3x + b. plug in the point to solve for b

-6 = -3(7) + b

b = 21-6 = 15