Question

find the slope of a line perpendicular to the line whose equation is 15x - 18y = -486. fully simplify your answer. answer attempt 1 out of 3 submit answer watch video show examples

Explanation:

Step1: Find slope of given line

First, rewrite the equation \(15x - 18y=-486\) in slope - intercept form \(y = mx + b\) (where \(m\) is the slope).
Start with \(15x-18y=-486\).
Subtract \(15x\) from both sides: \(- 18y=-15x - 486\).
Divide each term by \(-18\): \(y=\frac{-15x}{-18}+\frac{-486}{-18}\).
Simplify: \(y=\frac{5}{6}x + 27\). So the slope of the given line (\(m_1\)) is \(\frac{5}{6}\).

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes \(m_1\times m_2=- 1\). Let the slope of the perpendicular line be \(m_2\).
We know \(m_1 = \frac{5}{6}\), so \(\frac{5}{6}\times m_2=-1\).
Solve for \(m_2\): \(m_2=-\frac{6}{5}\).

Answer:

\(-\frac{6}{5}\)