Find the angular coefficient of the line represented by \(2y - 3x = 6\).

To find the angular coefficient (or slope) of the line represented by the equation (2y - 3x = 6), we need to first rearrange this equation into the slope-intercept form, which is (y = mx + b), where (m) is the angular coefficient.

Starting with the given equation:

[

2y - 3x = 6

]

We can isolate (y) by following these steps:

1. Add (3x) to both sides:

[

2y = 3x + 6

]

2. Next, divide every term by (2) to solve for (y):

[

y = \frac{3}{2}x + 3

]

From this form, we can clearly see that the angular coefficient, or slope (m), is (\frac{3}{2}). This coefficient tells us how much (y) changes for a unit change in (x): for every increase of 1 in (x), (y) increases by (\frac{3}{2}).

Thus, the angular coefficient of the line represented by the equation (2y -