The graph of 2x+3y =6 is a line which meets the y axis at the point

Options

A. only one
B. two
C. three
D. infinitely many

Answer

To find the point where the graph of the equation \(2x + 3y = 6\) meets the y-axis, we can follow these steps:

### Step 1: Understand the y-axis
The y-axis is where \(x = 0\). To find the point where the line intersects the y-axis, we will substitute \(x = 0\) into the equation.

**Hint:** Remember that any point on the y-axis has an x-coordinate of 0.

### Step 2: Substitute \(x = 0\) into the equation
Substituting \(x = 0\) into the equation \(2x + 3y = 6\):

\[ 2(0) + 3y = 6 \]

This simplifies to:

\[ 3y = 6 \]

**Hint:** Always simplify the equation after substituting values.

### Step 3: Solve for \(y\)
Now, we can solve for \(y\) by dividing both sides of the equation by 3:

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

**Hint:** When you have a coefficient in front of \(y\), you can isolate \(y\) by dividing.

### Step 4: Identify the point of intersection
The point where the line intersects the y-axis is \((0, 2)\).

**Hint:** The format of the point is \((x, y)\); since we set \(x = 0\), the y-coordinate is what we calculated.

### Step 5: Conclusion
Thus, the graph of the equation \(2x + 3y = 6\) meets the y-axis at the point \((0, 2)\).

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