Question

which statement explains how the lines $2x + y = 4$ and $y = \frac{1}{2}x + 4$ are related?\
\
\bigcirc they are parallel.\
\bigcirc they are perpendicular.\
\bigcirc they are the same line.\
\bigcirc they are not related.

Explanation:

Step1: Convert to slope-intercept form

Rewrite $2x + y = 4$ as $y = -2x + 4$. The second line is already $y = \frac{1}{2}x + 4$.

Step2: Identify slopes

Slope of first line: $m_1 = -2$; Slope of second line: $m_2 = \frac{1}{2}$

Step3: Check perpendicular condition

Calculate product: $m_1 \times m_2 = -2 \times \frac{1}{2} = -1$

Answer:

B. They are perpendicular.