Question

question
find the slope of a line perpendicular to the line whose equation is 3x - 5y = 45. fully simplify your a

Explanation:

Step1: Convert to slope - intercept form

We start with the equation \(3x - 5y=45\). We want to solve for \(y\) to get it in the form \(y = mx + b\) (where \(m\) is the slope).
Subtract \(3x\) from both sides: \(- 5y=-3x + 45\).
Then divide each term by \(-5\): \(y=\frac{-3x}{-5}+\frac{45}{-5}\), which simplifies to \(y=\frac{3}{5}x - 9\). The slope of the given line \(m_1=\frac{3}{5}\).

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 \(m_1 = \frac{3}{5}\), so we solve for \(m_2\): \(m_2=-\frac{1}{m_1}\).
Substitute \(m_1=\frac{3}{5}\) into the formula: \(m_2 =-\frac{5}{3}\).

Answer:

\(-\frac{5}{3}\)