Question

(04.02 lc) 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: Find slope of first line

Rewrite \(2x + y = 4\) in slope - intercept form (\(y=mx + b\), where \(m\) is the slope).
Subtract \(2x\) from both sides: \(y=-2x + 4\). So the slope \(m_1=-2\).

Step2: Find slope of second line

The second line is \(y=\frac{1}{2}x + 4\), so its slope \(m_2=\frac{1}{2}\).

Step3: Check relationship between slopes

Two lines are perpendicular if the product of their slopes is \(- 1\).
Calculate \(m_1\times m_2=(-2)\times\frac{1}{2}=-1\).

Answer:

They are perpendicular.