To graph the equation \( x - y = 6 \) in the form \( y = mx + b \), we first need to rearrange the equation into slope-intercept form.
Starting with the equation:
\[ x - y = 6 \]
We can solve for \( y \):
\[ -y = -x + 6 \]
Multiplying through by -1 gives:
\[ y = x - 6 \]
This means that the slope \( m = 1 \) and the y-intercept \( b = -6 \).
Next, we can identify some points based on this equation. For example:
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When \( x = 0 \): \[ y = 0 - 6 = -6 \quad \text{(Point: (0, -6))} \]
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When \( x = 1 \): \[ y = 1 - 6 = -5 \quad \text{(Point: (1, -5))} \]
With these points (0, -6) and (1, -5), we can now analyze the provided options to find matches:
- Graph 1 has the points (0, -6) and (1, -5), which perfectly matches our calculations.
- Graph 2 has (0, -4) and (1, -10), which does not match.
- Graph 3 has (0, 0) and (6, 6), which does not match.
- Graph 4 has (0, 3) and (3, 2), which does not match.
Therefore, the correct graph is Graph 1: (0, -6) and (1, -5).
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