Exercise 15 Page 191

Two lines are parallel if their slopes are identical. To tell if two lines are perpendicular, we check if their slopes are negative reciprocals. Let's tackle these one at a time.

Parallel Lines

For this exercise, we have been given two points on each line, so we have enough information to calculate their slopes using the Slope Formula. Note that when choosing points to substitute for $(x_1,y_1)$ and $(x_2,y_2),$ it does not matter which points on the line you choose, since the result will be the same. Let's start with line $a,$ which passes through $(\text{-}2,1)$ and $(0,3).$