Question

line f passes through points (1, 3) and (8, 9). line g is perpendicular to f. what is the slope of line g? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Find slope of line f

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(1, 3)$ and $(8, 9)$, $x_1 = 1, y_1 = 3, x_2 = 8, y_2 = 9$. So slope of f is $\frac{9 - 3}{8 - 1} = \frac{6}{7}$.

Step2: Find slope of line g (perpendicular)

Perpendicular slopes are negative reciprocals. So slope of g is $-\frac{7}{6}$ (negative reciprocal of $\frac{6}{7}$).

Answer:

$-\frac{7}{6}$