A person standing at the junction (crossing) of two straight paths represented by the equations `2x - 3y +4 = 0`and `3x + 4y - 5`= 0 wants to reach the path whose equation is `6x - 7y + 8 = 0` in the least time. Find equation of the path equation that he should follow.

Explanation

To solve the problem step by step, we need to find the equation of the path that the person should follow to reach the line \(6x - 7y + 8 = 0\) in the least time. This involves finding the intersection point of the two given lines and then determining the equation of the line that is perpendicular to the given line and passes through that intersection point.

### Step 1: Find the intersection point of the two lines

The equations of the two lines are:
1. \(2x - 3y + 4 = 0\) (let's call this Equation 1)
2. \(3x + 4y - 5 = 0\) (let's call this Equation 2)

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