Question

find the slope of a line perpendicular to the line whose equation is 5x + 6y = -54. fully simplify your answer. answer attempt 1 out of 2

Explanation:

Step1: Find slope of given line

Rewrite \(5x + 6y=-54\) in slope - intercept form \(y = mx + b\) (where \(m\) is the slope).
Subtract \(5x\) from both sides: \(6y=-5x - 54\).
Divide by 6: \(y=-\frac{5}{6}x - 9\). So the slope of the given line \(m_1 = -\frac{5}{6}\).

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 have \(-\frac{5}{6}\times m_2=-1\).
Solve for \(m_2\): \(m_2=\frac{-1}{-\frac{5}{6}}=\frac{6}{5}\).

Answer:

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