Question

what is the slope of a line that is perpendicular to the line $y = 8x + 5$?\
$-8$\
$8$\
$-\frac{1}{8}$\
$\frac{1}{8}$

Explanation:

Step1: Recall the slope of the given line

The equation of the given line is in the slope - intercept form \(y = mx + b\), where \(m\) is the slope. For the line \(y=8x + 5\), the slope \(m_1=8\).

Step2: Use the formula for slopes of perpendicular lines

If two lines are perpendicular, the product of their slopes \(m_1\) and \(m_2\) is \(- 1\), i.e., \(m_1\times m_2=-1\). We know \(m_1 = 8\), so we can solve for \(m_2\):
\[

$$\begin{align*} 8\times m_2&=-1\\ m_2&=-\frac{1}{8} \end{align*}$$

\]

Answer:

\(-\frac{1}{8}\) (corresponding to the option with value \(-\frac{1}{8}\))