First, let's start by finding the slope of the provided line. The provided line exists in standard form, which is 3x - 2y = 10. Transcribe this to the slope-intercept form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
The equation in slope-intercept form will be:
y = (3/2)x - 5
Hence, the slope (m1) of the given line is 3/2.
We know that parallel lines have the same slope. Therefore, the slope (m2) of the new line that we want to find will also be 3/2.
We're given that this line passes through the point (4, 2). This is given as (x1, y1).
We can now use the point-slope formula y - y1 = m(x - x1) to find the equation of the line. Substituting in the given point and the slope, we get:
y - 2 = 3/2 * (x - 4)
In order to write this in slope intercept form, we can think of it as y - 2 = 1.5x - 6.
By arranging this equation, we get:
y = 1.5x - 4
Hence, the equation of the line that is parallel to the given line and passes through the point (4, 2) is y = 1.5x - 4.