Find the equation of the line that passes through (5,-3) and perpendicular to 3x+2y=3

We find the slope of the given line in the form y = mx + c to find its slope:

3x + 2y = 3

2y = - 3x + 3

y = (-3/2)x = 3

Therefore the slope of the given line is -3/2.

Slope of the a line perpendicular to another is inverse of the slope of first line, multiplied by -1

Therefore slope of perpendicular to given line = -1/(-3/2) = 2/3

Therefore the equation of the perpendicular may be given as:

y = (2/3)x + c

This perpendicular line passes through the point (5, -3). Therefore to get the value of c in its equation we substitute the values of the coordinates of the point in the equation.

- 3 = (2/3)5 + c

- 3 = 10/3 + c

c = - 3 - 10/3 = - 19/3

Substituting this value in equation of perpendicular:

y = (2/3)x - 19/3

Multiplying this equation by -3, and taking all the terms on left hand side we get:

2x - 3y - 19 = 0