Find the y-intercept of the line \( 2y - 3x = 6 \).

To determine the y-intercept of the line represented by the equation ( 2y - 3x = 6 ), we need to find the value of ( y ) when ( x ) is equal to 0. The y-intercept occurs where the line crosses the y-axis.

We can start by substituting ( x = 0 ) into the equation:

[

2y - 3(0) = 6

]

This simplifies to:

[

2y = 6

]

Next, to isolate ( y ), divide both sides of the equation by 2:

[

y = \frac{6}{2} = 3

]

Thus, the y-intercept of the line is ( 3 ). This means that when the line crosses the y-axis, it does so at the point ( (0, 3) ).

This confirms that the correct answer is indeed ( 3 ), as it represents the y-coordinate of the point where the line crosses the y-axis.