Find the equation of a line passing through `(4,5)` and perpendicular to the line `2x+3y=5`.

Answer

To find the equation of a line passing through the point (4, 5) and perpendicular to the line given by the equation \(2x + 3y = 5\), we can follow these steps:

### Step 1: Find the slope of the given line
The equation of the line is given in standard form \(Ax + By + C = 0\). We can rewrite the equation \(2x + 3y = 5\) in slope-intercept form \(y = mx + b\) to find the slope.

1. Rearranging the equation:
\[ 3y = -2x + 5 \]
\[ y = -\frac{2}{3}x + \frac{5}{3} \]

The slope \(m_1\) of the given line is \(-\frac{2}{3}\).