First, let's find the slope of the line 5x + 3y = 6:
5x + 3y = 6
3y = 6 - 5x
y = 6/3 - 5x/3
y = (-5/3)x + 2
The equation is now in the form y = mx + b where m is the slope and b is the y-intercept.
Therefore, slope is -5/3.
This is important because parallel lines have the same slope.
We are looking for the equation of the line that passes through the point (6,-2) and has a slope of -5/3.
We can use point slope form:
y - y1 = m(x - x1) where m is the slope and (x1,y1) is a point on the line.
Therefore an equation of the line is:
y - (-2) = (-5/3)(x - 6)
or y + 2 = (-5/3)(x - 6)
This equation can be re-arranged algebraically if slope-intercept form or standard form (ax + by = c) or some other form are requested.