Question

The graph of the linear equation \(2x + 3y = 6\) is a line which meets the y-axis at the point :

• A. (0, 2)
• B. (2, 0)
• C. (3, 0)
• D. (0, 3)

Hint:

A point on the y-axis must have the format \((0, y)\). This immediately eliminates options (B) and (C).
For the remaining options, plug in the coordinates:
For \((0, 2)\): \(2(0) + 3(2) = 6\), which matches perfectly.
This is a quick and foolproof way to verify coordinate questions.

Answer 1

The Correct Option is A

Step 1: Use the intercept form of a line instead of substitution.
Any line can be written in intercept form $\frac{x}{a} + \frac{y}{b} = 1$, where $a$ is the x-intercept and $b$ is the y-intercept.
Step 2: Convert the given equation to this form.
Starting from $2x + 3y = 6$, divide every term by 6: \[ \frac{2x}{6} + \frac{3y}{6} = 1 \quad \Rightarrow \quad \frac{x}{3} + \frac{y}{2} = 1 \]
Step 3: Read off the intercepts directly.
Comparing with $\frac{x}{a} + \frac{y}{b} = 1$, we get $a = 3$ and $b = 2$. The y-intercept is the point where $x = 0$, which is $(0, b)$.
Step 4: State the point.
So the line meets the y-axis at $(0, 2)$, the same point we would find by direct substitution of $x = 0$.
\[ \boxed{(0, 2)} \]