Question

applying theorems to determine slope try it if line b is perpendicular to line a, and line c is perpendicular to line a, what is the slope of line c? ( m_c = ) box

Explanation:

Step1: Find slope of line \( a \)

Points on line \( a \): \((-3, 3)\) and \((3, -3)\).
Slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
\( m_a = \frac{-3 - 3}{3 - (-3)} = \frac{-6}{6} = -1 \)

Step2: Slope of perpendicular lines

If two lines are perpendicular, their slopes multiply to \(-1\) (\( m_1 \cdot m_2 = -1 \)).
Line \( b \) is perpendicular to \( a \), so \( m_b \cdot (-1) = -1 \Rightarrow m_b = 1 \).

Line \( c \) is also perpendicular to \( a \). Lines perpendicular to the same line are parallel, so \( m_c = m_b \).

Answer:

\( 1 \)