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: Understanding the Question:
This question is from the topic of Linear Equations in Two Variables and Coordinate Geometry.
We need to find the point where the line represented by the equation \(2x + 3y = 6\) intersects the y-axis.

Step 2: Key Formula or Approach:
Any point on the y-axis has its x-coordinate equal to zero (\(x = 0\)).
To find the y-intercept of a line, we substitute \(x = 0\) into the equation of the line and solve for \(y\).

Step 3: Detailed Explanation:
Given equation of the line:
\[ 2x + 3y = 6 \]
Since the line meets the y-axis, we set the x-coordinate to zero:
\[ x = 0 \]
Substitute \(x = 0\) into the equation:
\[ 2(0) + 3y = 6 \]
\[ 0 + 3y = 6 \]
\[ 3y = 6 \]
Divide both sides by 3:
\[ y = \frac{6}{3} \]
\[ y = 2 \]
Therefore, the point of intersection on the y-axis is \((0, 2)\).

Step 4: Final Answer:
The line meets the y-axis at the point \((0, 2)\).