Draw the graph of 2x - 3y + 6 = 0. Hence, find the co-ordinates of points where the graph drawn meets the co-ordinate axes.

Answer

To solve the problem step by step, we will first rearrange the equation and then find the points where the graph intersects the coordinate axes.

### Step 1: Rearranging the Equation
The given equation is:
\[ 2x - 3y + 6 = 0 \]

We can rearrange it to express \(y\) in terms of \(x\):
\[ -3y = -2x - 6 \]
\[ 3y = 2x + 6 \]
\[ y = \frac{2}{3}x + 2 \]

### Step 2: Finding the Y-Intercept
To find the point where the graph meets the y-axis, we set \(x = 0\):
\[ y = \frac{2}{3}(0) + 2 = 2 \]
So, the y-intercept is at the point \((0, 2)\).

### Step 3: Finding the X-Intercept
To find the point where the graph meets the x-axis, we set \(y = 0\):
\[ 0 = \frac{2}{3}x + 2 \]
\[ \frac{2}{3}x = -2 \]
\[ x = -2 \times \frac{3}{2} = -3 \]
So, the x-intercept is at the point \((-3, 0)\).

### Step 4: Plotting the Points
Now we have two points:
1. Y-intercept: \((0, 2)\)
2. X-intercept: \((-3, 0)\)

### Step 5: Drawing the Graph
We can plot these points on a graph:
- Plot the point \((0, 2)\) on the y-axis.
- Plot the point \((-3, 0)\) on the x-axis.
- Draw a straight line through these two points to represent the equation \(2x - 3y + 6 = 0\).

### Conclusion
The graph of the equation meets the coordinate axes at the points:
- Y-intercept: \((0, 2)\)
- X-intercept: \((-3, 0)\)