Question

any line perpendicular to the line $y = 2x + 4$ has a slope of -2.
true
false

Explanation:

Step1: Recall slope of perpendicular lines

For two perpendicular lines with slopes \(m_1\) and \(m_2\), the relationship is \(m_1\times m_2=- 1\).

Step2: Find slope of given line

The line \(y = 2x+4\) is in slope - intercept form \(y=mx + b\), where \(m\) is the slope. So the slope of the line \(y = 2x + 4\) is \(m_1=2\).

Step3: Calculate slope of perpendicular line

Let the slope of the perpendicular line be \(m_2\). Using the formula \(m_1\times m_2=-1\), substitute \(m_1 = 2\) into it: \(2\times m_2=-1\). Solve for \(m_2\), we get \(m_2=-\frac{1}{2}\), not \(- 2\).

Answer:

False