(a). A fence runs along y = -\frac{1}{2}x + 6. Charlie is adding a new fence section, parallel to the...

(a). A fence runs along y = -\frac{1}{2}x + 6. Charlie is adding a new fence section, parallel to the first. The new section passes through (8, -3). Charlie's driveway is modeled by y = \frac{5}{3}x - 4. A drainage pipe crosses the driveway perpendicular to it at (10, 3). Help Charlie find the equation of the new fence section and the equation of the drainage pipe so that he is able to correctly record the new additions to his blueprint.
(b). A sidewalk is modeled by 3x - y = 2. A support beam lies along x + 2y = 10. Determine whether the support beam is parallel to, perpendicular to, or neither parallel nor perpendicular to the sidewalk. Justify your answer.