Question

question
find the slope of a line perpendicular to the line whose equation is $9x + 3y = 36$. fully simplify your answer.

Explanation:

Step1: Convert to slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope. Start with the given equation \(9x+3y = 36\).
Subtract \(9x\) from both sides: \(3y=-9x + 36\).
Divide each term by 3: \(y=\frac{-9x + 36}{3}=-3x + 12\). The slope of the given line, \(m_1\), is \(- 3\).

Step2: Find the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes is \(-1\), i.e., \(m_1\times m_2=-1\).
We know \(m_1=-3\), so substitute into the formula: \(-3\times m_2=-1\).
Solve for \(m_2\): \(m_2=\frac{-1}{-3}=\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)