Draw the graph of the equation, `2x+y=6`
find the coordinates of the point where the graph cuts the x-axis.

Answer

To solve the problem of drawing the graph of the equation \(2x + y = 6\) and finding the coordinates of the point where the graph cuts the x-axis, we can follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
We start with the equation:
\[ 2x + y = 6 \]
To express \(y\) in terms of \(x\), we can rearrange the equation:
\[ y = 6 - 2x \]

### Step 2: Find the y-intercept
To find the y-intercept, we set \(x = 0\):
\[ y = 6 - 2(0) = 6 \]
Thus, the y-intercept is the point \((0, 6)\).

### Step 3: Find the x-intercept
To find the x-intercept, we set \(y = 0\):
\[ 0 = 6 - 2x \]
Solving for \(x\):
\[ 2x = 6 \implies x = \frac{6}{2} = 3 \]
Thus, the x-intercept is the point \((3, 0)\).

### Step 4: Plot the points on the graph
Now, we have two points:
1. The y-intercept \((0, 6)\)
2. The x-intercept \((3, 0)\)

### Step 5: Draw the graph
On a graph paper, plot the points \((0, 6)\) and \((3, 0)\). Draw a straight line through these points, which represents the equation \(2x + y = 6\).

### Conclusion
The coordinates of the point where the graph cuts the x-axis are \((3, 0)\).

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