find the equations of the lines to the line whose equations is

y-17 / x -13 = -3 /2

If these lines each pass through the point (6,-5)

Gracias`

To find the equations of the lines that pass through the given point (6,-5) and are parallel and perpendicular to the given line, you can follow these steps:

Step 1: Convert the given equation to the standard form of a linear equation (y = mx + b).
First, let's simplify the given equation:
(y - 17)/(x - 13) = -3/2

To eliminate the fractions, multiply both sides of the equation by 2(x - 13):
2(y - 17) = -3(x - 13)

Simplify further:
2y - 34 = -3x + 39
2y + 3x = 73 (Standard form of the equation)

Step 2: Determine the slope of the given line.
The coefficient of x in the standard form equation represents the slope. Hence, the slope of the given line is -3/2.

Step 3: Determine the slope of the lines that are parallel and perpendicular to the given line.
Since parallel lines have equal slopes, the parallel line will also have a slope of -3/2. Perpendicular lines have negative reciprocal slopes, so the perpendicular line will have a slope of 2/3.

Step 4: Use the point-slope form of a linear equation to find the equations of the lines.
For the line parallel to the given line, using the point (6, -5), the equation can be written as:
y - (-5) = (-3/2)(x - 6)
y + 5 = (-3/2)(x - 6)
2(y + 5) = -3(x - 6)
2y + 10 = -3x + 18
2y + 3x = 8 (Equation of the parallel line)

For the line perpendicular to the given line, using the point (6, -5), the equation can be written as:
y - (-5) = (2/3)(x - 6)
y + 5 = (2/3)(x - 6)
3(y + 5) = 2(x - 6)
3y + 15 = 2x - 12
2x - 3y = 27 (Equation of the perpendicular line)

So, the equation of the line parallel to the given line is 2y + 3x = 8, and the equation of the line perpendicular to the given line is 2x - 3y = 27.