At what point does the straight line 4x - 3y = -6 intersect the y-axis? Give your answer as an ordered pair (x, y).

Introduction / Context:
This question tests your understanding of intercepts of a straight line on the coordinate axes. Finding the y intercept from an equation in standard form is a basic and important skill in coordinate geometry. It is often used to sketch graphs quickly and to interpret linear relationships.

Given Data / Assumptions:

• Equation of the line: 4x - 3y = -6.
• We need the point where the line meets the y axis.
• On the y axis, the x coordinate is always 0.
• We must present the answer as an ordered pair (x, y).

Concept / Approach:
The y axis consists of all points where x = 0. To find the y intercept of a line, we set x = 0 in the line's equation and solve for y. The resulting value of y, together with x = 0, gives the intercept coordinate. This process is simple substitution followed by solving a linear equation in one variable.

Step-by-Step Solution:
Step 1: Start with the line equation 4x - 3y = -6. Step 2: At the y axis, x = 0. Substitute x = 0 into the equation. This gives 4 * 0 - 3y = -6, so -3y = -6. Step 3: Solve for y: divide both sides by -3 to get y = (-6) / (-3) = 2. Step 4: Therefore the y intercept is the point (0, 2).

Verification / Alternative check:
We can check by substituting the point (0, 2) back into the original equation. Substitute x = 0 and y = 2: 4 * 0 - 3 * 2 = 0 - 6 = -6, which matches the right hand side of the equation. This confirms that (0, 2) lies on the line and is indeed the point where the line crosses the y axis.

Why Other Options Are Wrong:
Option B (0, 3/2): Substituting y = 3/2 gives 4 * 0 - 3 * (3/2) = -9/2, which is not equal to -6. Option C (2, 0): This is a point on the x axis, not the y axis, since its x coordinate is 2. Option D (3/2, 0): This is also on the x axis and does not represent a y intercept. Option E (0, -2): Substituting y = -2 gives 4 * 0 - 3 * (-2) = 6, which does not equal -6.

Common Pitfalls:
A common mistake is to confuse x intercept and y intercept, substituting y = 0 instead of x = 0. Another issue is sign errors when solving the equation, especially with negative coefficients. Always remember that the y intercept has x = 0, and carefully substitute and solve to avoid sign mistakes.

Final Answer:
The line intercepts the y axis at the point (0, 2).