The equation of the straight line perpendicular to 5x-2y=7 and passing through the point of intersection of the lines 2x + 3y =1 and 3x +4y =6 is

Options

A. 2x+5y +17=0
B. 2x+5y -17=0
C. 2x -5y+17=0
D. 2x -5y =17

Explanation

To find the equation of the straight line that is perpendicular to the line given by the equation \(5x - 2y = 7\) and passes through the point of intersection of the lines \(2x + 3y = 1\) and \(3x + 4y = 6\), we can follow these steps:

### Step 1: Find the slope of the given line
The first step is to rewrite the equation of the line \(5x - 2y = 7\) in slope-intercept form \(y = mx + c\).

1. Rearranging the equation:
\[ 2y = 5x - 7 \]
\[ y = \frac{5}{2}x - \frac{7}{2} \]

2. From this, we can see that the slope \(m\) of the line is \(\frac{5}{2}\).