To determine which graph represents the equation \(x - y = 1\), we can rearrange it into slope-intercept form \(y = mx + b\):
Starting with: \[ x - y = 1 \] We can rearrange it to solve for \(y\): \[ -y = -x + 1 \] \[ y = x - 1 \]
This shows that the line has a slope of \(1\) and a y-intercept of \(-1\). Therefore, the line will pass through the point \((0, -1)\).
To find another point on the line, we can evaluate it at \(x = 1\): \[ y = 1 - 1 = 0 \] So another point on the line is \((1, 0)\).
Now, we can check the options:
- A coordinate plane with a line passing through (0, 1) and (1, 0): This does not match.
- A coordinate plane with a line passing through (0, -2) and (0, 1): This does not match.
- A coordinate plane with a line passing through (0, -1) and (1, 0): This matches.
- A coordinate plane with a line passing through (-1, 0) and (0, -1): This does not match.
Thus, the correct graph for the equation \(x - y = 1\) is the one that passes through \((0, -1)\) and \((1, 0)\).
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