To determine if the statements regarding the graph of the equation \(3x - y = 10\) are correct, we should first convert the equation into slope-intercept form (\(y = mx + b\)), where \(m\) is the slope and \(b\) is the y-intercept.
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Start with the equation: \[ 3x - y = 10 \]
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Solve for \(y\): \[ -y = -3x + 10 \] \[ y = 3x - 10 \]
From this form, we can see that:
- The slope \(m\) is 3.
- The y-intercept \(b\) is -10, which is the point \((0, -10)\).
Now let's evaluate the options provided:
- Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, − 10). (Incorrect: Slope is 3, not -3.)
- No, it is not the correct graph because the slope is −3 and the y-intercept is (0, − 10). (Incorrect: Slope is 3, not -3.)
- Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, − 10). (Correct: Slope is 3 and y-intercept is -10.)
- No, it is not the correct graph because the slope is 3 and the y-intercept is (0, − 10). (Incorrect: This statement contradicts the correct information.)
Thus, the correct statement is: Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, − 10).