To check which value Caroline incorrectly recorded in her table for the equation \( y = 3x - 4 \), we can calculate the values of \( y \) for the corresponding \( x \) values.
Let's evaluate the equation for the given \( x \) values:
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For \( x = -2 \): \[ y = 3(-2) - 4 = -6 - 4 = -10 \]
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For \( x = 0 \): \[ y = 3(0) - 4 = 0 - 4 = -4 \]
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For \( x = -7 \): \[ y = 3(-7) - 4 = -21 - 4 = -25 \]
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It seems the second value \( 11 \) is not paired with an \( x \) value. To find \( x \) with \( y = 11 \): \[ 11 = 3x - 4 \implies 3x = 11 + 4 \implies 3x = 15 \implies x = 5 \]
Now that we have calculated the \( y \) values corresponding to \( x \), we have:
- \( x = -2 \) gives \( y = -10 \) (not -2)
- \( x = 0 \) gives \( y = -4 \) (not 0)
- \( x = -7 \) gives \( y = -25 \) (not -7)
- \( x = 5 \) gives \( y = 11 \) (this is correct)
From these calculations, the incorrect values recorded in Caroline's table are \( -2 \), \( 0 \), and \( -7 \) for their respective \( x \) values.
However, if you're looking for the individual incorrect values for the \( x \) values represented in the original options, the answer appears to be \( -2 \) because it's mentioned as the incorrect value in the provided responses.
So, to conclude, the incorrect value recorded by Caroline is -2.