y-intercept of a line\nAt what point does the line 4x − 3y = −6 cut the y-axis?

Introduction / Context:
Intercepts are found by setting the other coordinate to zero. The y-intercept occurs where x = 0. Solve for y from the given linear equation to get the intercept point explicitly.

Given Data / Assumptions:

• Equation: 4x − 3y = −6
• At y-intercept, x = 0

Concept / Approach:
Substitute x = 0 to get −3y = −6 ⇒ y = 2. The y-intercept point is (0, 2).

Step-by-Step Solution:

Verification / Alternative check:
Rearrange to slope–intercept form: −3y = −4x − 6 ⇒ y = (4/3)x + 2. Intercept is 2, confirming (0, 2).

Why Other Options Are Wrong:
(0, 3/2) corresponds to y = 1.5, not satisfying the equation; (2, 0) and (3/2, 0) are x-intercepts candidate points, not y-intercepts here.

Common Pitfalls:
Confusing x- and y-intercepts or sign slips when isolating y are typical mistakes.

Final Answer:
(0,2)