Draw the graph of the linear equation 2x+3y=6 find out the coordiantes of the points where the line intersects at x axis and y axis

Answer

To solve the problem step by step, we will draw the graph of the linear equation \(2x + 3y = 6\) and find the coordinates of the points where the line intersects the x-axis and y-axis.

### Step 1: Write the equation of the line
The given linear equation is:
\[ 2x + 3y = 6 \]

### Step 2: Find the y-intercept
To find the y-intercept, we set \(x = 0\) in the equation:
\[ 2(0) + 3y = 6 \]
This simplifies to:
\[ 3y = 6 \]
Dividing both sides by 3 gives:
\[ y = 2 \]
Thus, the y-intercept is at the point \((0, 2)\).

### Step 3: Find the x-intercept
To find the x-intercept, we set \(y = 0\) in the equation:
\[ 2x + 3(0) = 6 \]
This simplifies to:
\[ 2x = 6 \]
Dividing both sides by 2 gives:
\[ x = 3 \]
Thus, the x-intercept is at the point \((3, 0)\).

### Step 4: Plot the points
Now we will plot the points \((0, 2)\) and \((3, 0)\) on a graph:
- Start from the origin \((0, 0)\), move 2 units up to plot the point \((0, 2)\).
- From the origin, move 3 units to the right to plot the point \((3, 0)\).

### Step 5: Draw the line
Now, draw a straight line through the points \((0, 2)\) and \((3, 0)\). This line represents the equation \(2x + 3y = 6\).

### Step 6: Identify the intercepts
From the graph, we can see that the line intersects the y-axis at the point \((0, 2)\) and the x-axis at the point \((3, 0)\).

### Final Result
- The coordinates where the line intersects the y-axis is \((0, 2)\).
- The coordinates where the line intersects the x-axis is \((3, 0)\).

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