Find the slope of the line perpendicular to $4x-5y=\frac{9}{2}$

• A. $\frac{4}{5}$
• B. $\frac{9}{10}$
• C. $-\frac{9}{2}$
• D. $-\frac{5}{4}$

Answer: (D)

Verified step by step guidance

1. Start with the given equation of the line: \(4x - 5y = \frac{9}{2}\).
2. Rewrite the equation in slope-intercept form \(y = mx + b\) by isolating \(y\). First, subtract \$4x$ from both sides: \(-5y = -4x + \frac{9}{2}\).
3. Next, divide every term by \(-5\) to solve for \(y\): \(y = \frac{-4x}{-5} + \frac{\frac{9}{2}}{-5}\), which simplifies to \(y = \frac{4}{5}x - \frac{9}{10}\).
4. Identify the slope \(m\) of the given line from the slope-intercept form. Here, \(m = \frac{4}{5}\).
5. Recall that the slope of a line perpendicular to another is the negative reciprocal of the original slope. So, find the negative reciprocal of \(\frac{4}{5}\), which is \(-\frac{5}{4}\).