Question

Consider the point P = (2, 8) and the line L, given by the equation 6x - 3y = 15.

A. Write an equation in slope-intercept of the line passing through P and parallel to line L.

B. Write an equation in slope-intercept of the line passing through P and perpendicular to line L.

Answer 1

rewrite the given line to slope intercept form y = m x + b
m will be the slope
parallel lines have the same slope
the "new line " passes through the point (2, 8) this is your (x, y) put in the equation and solve for b, the intercept
write the general equation for the parallel line using m, b and any point (x, y)

B. for perpendicular lines the product of the slopes is -1
given the slope, m the slope of the perpendicular = -1/m
passing through ( 2, 8 ) you can calculate b, the intercept.
now write the general equation using m, b and (x, y)