Question

complete the statement. the slope of a line perpendicular to the line $y - 9 = 12(x + 2)$ is ______. \bigcirc 12 \bigcirc $\frac{1}{12}$ \bigcirc $-\frac{1}{12}$ \bigcirc -12

Explanation:

Step1: Identify the slope of the given line

The given line is in point - slope form \(y - y_1=m(x - x_1)\), where \(m\) is the slope. For the line \(y - 9 = 12(x + 2)\), the slope \(m_1\) of this line is \(12\).

Step2: Recall the relationship between 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 \(m_1 = 12\), and we need to find \(m_2\) (the slope of the line perpendicular to the given line).

Step3: Solve for the slope of the perpendicular line

From \(m_1\times m_2=-1\), substitute \(m_1 = 12\) into the equation:
\(12\times m_2=-1\)
To find \(m_2\), we divide both sides of the equation by \(12\):
\(m_2=-\frac{1}{12}\)

Answer:

\(-\frac{1}{12}\) (corresponding to the option \(-\frac{1}{12}\))