Find a general form of an equation of the line through the p

Find a general form of an equation of the line through the point A that satisfies the given condition.

A(5,4) perpindicular to the line 3x+2y=7

Can you show me each step and explain this process to me? I have a few questions that are similar and I am not sure where to start.

Thanks!

3x+2y=7

==> 2y = -3x + 7

==> y = (-3/2)x + 7/2

slope of given line = -3/2

Given line and required line are perpendicular

==> slope of required line = 2/3 (since product of slopes of perpendicular lines = -1)

equation of line passing through point (5 , 4) with slope 2/3 is

y - 4 = (2/3)(x - 5)

==> 3(y - 4) = 2x - 10

==> 2x - 3y = -2