Question

given the graph of line m
what would be the slope of line b which is perpendicular to line m?
a -\frac{5}{6}
b \frac{6}{5}
c \frac{5}{6}
d -\frac{6}{5}

Explanation:

Step1: Find slope of line m

Pick two points on line m, say (0, 5) and (6, 0). Using slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_m=\frac{0 - 5}{6 - 0}=-\frac{5}{6}$.

Step2: Use perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line b be $m_b$. Then $m_m\times m_b=-1$. Substitute $m_m = -\frac{5}{6}$ into the equation: $-\frac{5}{6}\times m_b=-1$. Solving for $m_b$, we get $m_b=\frac{6}{5}$.

Answer:

B. $\frac{6}{5}$