Question

line v is defined by y = 2x + 8. line w is perpendicular to line v in the xy - plane. what is the slope of line w?
a -1/10
b -1/2
c -1/8
d -1/4

Explanation:

Step1: Determine slope of line v

The equation of line v is $y = 2x+8$, which is in slope - intercept form $y=mx + b$ where $m$ is the slope. So the slope of line v, $m_v=2$.

Step2: Use perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line w be $m_w$. Then $m_v\times m_w=-1$. Substitute $m_v = 2$ into the equation: $2\times m_w=-1$. Solve for $m_w$: $m_w=-\frac{1}{2}$.

Answer:

B. $-\frac{1}{2}$