Question

line b passes through points (8, 1) and (10, 10). line c is perpendicular to b. what is the slope of line c? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Calculate slope of line b

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For line $b$ with points $(x_1,y_1)=(8,1)$ and $(x_2,y_2)=(10,10)$, we have $m_b=\frac{10 - 1}{10 - 8}=\frac{9}{2}$.

Step2: Find slope of line c

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line $c$ be $m_c$. Then $m_b\times m_c=-1$. Since $m_b = \frac{9}{2}$, we can solve for $m_c$: $m_c=-\frac{2}{9}$.

Answer:

$-\frac{2}{9}$