Consider the point (-6,3) and line l: 4x-3y=5. write an equation (a) for the line passing through this point and parallel to l, and (b) for the line passing through this point and perpendicular to l.

4x - 3y =5

3y = 4x - 5

y = 4/3 x - 5/3

Equation of the line passing through the point (-6,3) and parallel to L

a) Parallel lines have same slope so slope = 4/3

y - 3 = 4/3(x + 6)

y - 3 = 4/3 x + 8

y = 4/3 x + 11

Equation y = 4/3 x + 11

b) Perpendicular lines, slope is opposite and reciprocal so slope = -3/4

y - 3 = -3/4 (x + 6)

y - 3 = -3/4 x - 4.5

y = -3/4 x - 1.5

Equation y = -3/4 x - 1.5