Question

line f passes through points (8, 4) and (5, 2). line g passes through points (4, 5) and (6, 2). are line f and line g parallel or perpendicular?
parallel perpendicular neither

Explanation:

Step1: Calculate slope of line f

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
For line f with $(x_1,y_1)=(8,4)$ and $(x_2,y_2)=(5,2)$:
$m_f = \frac{2 - 4}{5 - 8} = \frac{-2}{-3} = \frac{2}{3}$

Step2: Calculate slope of line g

For line g with $(x_1,y_1)=(4,5)$ and $(x_2,y_2)=(6,2)$:
$m_g = \frac{2 - 5}{6 - 4} = \frac{-3}{2}$

Step3: Check parallel/perpendicular

Parallel: slopes equal ($\frac{2}{3}
eq \frac{-3}{2}$, no).
Perpendicular: product = -1:
$m_f \times m_g = \frac{2}{3} \times \frac{-3}{2} = -1$

Answer:

perpendicular