To determine if Annie's graph of the equation \(3x + y = 10\) is correct, we can convert the equation to slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the given equation:
\[ 3x + y = 10 \]
we can solve for \(y\):
\[ y = -3x + 10 \]
From this equation, we can see that the slope \(m\) is \(-3\) and the y-intercept \(b\) is \(10\).
Now let's evaluate the options:
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Option 1 states that Annie's y-intercept is correct but her slope is incorrect. This is false because both the y-intercept (10) and the slope (-3) are correct.
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Option 2 states that Annie's slope is correct but her y-intercept is incorrect. This is false as well because both values are actually correct.
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Option 3 states that Annie's graph is correct. This is true because both the slope and y-intercept calculated from the equation are consistent with the graph she created.
Therefore, the correct answer is:
3