Question

line f passes through points (7, 9) and (5, 12). line g passes through points (4, 6) and (7, 8). are line f and line g parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Calculate slope of line f

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For line f with points (7, 9) and (5, 12), $m_f = \frac{12 - 9}{5 - 7} = \frac{3}{-2} = -\frac{3}{2}$.

Step2: Calculate slope of line g

For line g with points (4, 6) and (7, 8), $m_g = \frac{8 - 6}{7 - 4} = \frac{2}{3}$.

Step3: Check parallel or perpendicular

Parallel lines have equal slopes, $-\frac{3}{2}
eq \frac{2}{3}$, so not parallel. Perpendicular lines have slopes that multiply to -1: $(-\frac{3}{2}) \times (\frac{2}{3}) = -1$. So they are perpendicular.

Answer:

perpendicular