Parallel and Perpendicular Equations

Which lines are parallel? Give proof.

Which lines are perpendicular? Give proof.

Give the slopes and tell what the relationship between the lines are. Line a goes through points (1,0) and (7,4) Line b goes through points (7,0) and (3,6)

Give the slopes and tell what the relationship between the lines are. Line a goes through points (-3,1) and (-7,-2) Line b goes through points (2,-1) and (8,4)

Give the slopes and tell what the relationship between the lines are. Line a goes through points (10,5) and (-8,9) Line b goes through points (2,-4) and (11,-6)

Write an equation of the line passing through point P(0, −1) that is parallel to the line y = −2x+3.

Write an equation of the line passing through point P(0, 0) that is perpendicular to the line  y = −9x−1.

On a trip to New York City, my partner and I took the approximate route shown above for the day's activities. We started at Radio City Music Hall (point 1), and went to Gershwin Theater (point 2). After that we went to Ellen's Stardust Diner (point 3) and ended at Rockefeller Center (point 4). Assume the roads and paths are straight and the city is properly laid out on a grid (the segments are added in as approximations). Which parts of the journey were parallel and which were perpendicular?