If the graph of the equation `2x+3y=6` form a triangle with coordinates axis, then the area of triangle will be

Options

A. 2 sq units
B. 3 sq units
C. 6 sq units
D. 1 sq units

Answer

To find the area of the triangle formed by the graph of the equation \(2x + 3y = 6\) with the coordinate axes, we can follow these steps:

### Step 1: Find the x-intercept
To find the x-intercept, set \(y = 0\) in the equation \(2x + 3y = 6\).

\[ 2x + 3(0) = 6 \implies 2x = 6 \implies x = \frac{6}{2} = 3 \]

Thus, the x-intercept is at the point \((3, 0)\).

### Step 2: Find the y-intercept
To find the y-intercept, set \(x = 0\) in the equation \(2x + 3y = 6\).

\[ 2(0) + 3y = 6 \implies 3y = 6 \implies y = \frac{6}{3} = 2 \]

Thus, the y-intercept is at the point \((0, 2)\).

### Step 3: Determine the vertices of the triangle
The triangle formed by the line and the coordinate axes has its vertices at:
1. \((0, 0)\) - the origin
2. \((3, 0)\) - the x-intercept
3. \((0, 2)\) - the y-intercept

### Step 4: Calculate the area of the triangle
The area \(A\) of a triangle formed by the x-axis and y-axis can be calculated using the formula:

\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

In this case, the base is the x-intercept (3 units) and the height is the y-intercept (2 units).

\[ A = \frac{1}{2} \times 3 \times 2 = \frac{6}{2} = 3 \]

### Conclusion
The area of the triangle formed by the graph of the equation \(2x + 3y = 6\) with the coordinate axes is \(3\) square units.