To determine whether the graph corresponds to the equation \(3x - y = 10\), we need to rewrite the equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the equation:
\[ 3x - y = 10 \]
We can rearrange this to isolate \(y\):
\[ -y = -3x + 10 \]
Multiply both sides by -1:
\[ y = 3x - 10 \]
From this, we can see that:
- The slope \(m\) is 3.
- The y-intercept is \((0, -10)\).
Now, to evaluate the answer choices:
- A states the slope is -3, which is incorrect.
- B states the slope is 3 (correct) but the y-intercept is also wrong, as it should be (0, -10).
- C states the slope is 3 and the y-intercept is (0, -10), which is correct.
- D states the slope is -3, which is also incorrect.
The correct answer is:
C. Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).
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