Question

1
which equation is perpendicular to the line $y = -\frac{1}{2}x + 4$
a $y = -\frac{1}{2}x + 4$
b $y = \frac{1}{2}x - 1$
c $y = 2x - 1$
d $y = -2x + 2$

Explanation:

Step1: Identify given line slope

The given line is $y = -\frac{1}{2}x + 4$, so its slope $m_1 = -\frac{1}{2}$.

Step2: Find perpendicular slope

Perpendicular slopes multiply to $-1$. Let $m_2$ be the perpendicular slope:
$$m_1 \times m_2 = -1$$
$$-\frac{1}{2} \times m_2 = -1$$
Solve for $m_2$: $m_2 = 2$.

Step3: Match slope to options

Look for the equation with slope $2$. Option C: $y=2x-1$ has slope $2$.

Answer:

C. $y = 2x - 1$