Draw the graph for each equation given below:
`3x+2y=6`
In each case find the co-ordinate of the points where the graph (line) drawn meets the co-ordinate axes.

Answer

To solve the equation \(3x + 2y = 6\) and draw its graph, we will follow these steps:

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

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

So, the x-intercept is at the point \((2, 0)\).

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

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

So, the y-intercept is at the point \((0, 3)\).

### Step 3: Plot the points
Now we have two points:
- The x-intercept \((2, 0)\)
- The y-intercept \((0, 3)\)

### Step 4: Draw the graph
Using the points \((2, 0)\) and \((0, 3)\), we can draw a straight line that passes through these two points.

1. Start by plotting the point \((2, 0)\) on the x-axis.
2. Next, plot the point \((0, 3)\) on the y-axis.
3. Finally, draw a straight line through these two points, extending it in both directions.

### Final Graph
The graph of the equation \(3x + 2y = 6\) is a straight line that intersects the x-axis at \((2, 0)\) and the y-axis at \((0, 3)\).

### Summary of Points of Intersection
- **X-intercept**: \((2, 0)\)
- **Y-intercept**: \((0, 3)\)

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