To find the equation of a line in standard form that passes through the point (2, 9) with a slope of 12, we can start by using the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is the point (2, 9) and \( m \) is the slope (12):
\[ y - 9 = 12(x - 2) \]
Now, we'll simplify this equation:
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Distribute the slope: \[ y - 9 = 12x - 24 \]
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Add 9 to both sides: \[ y = 12x - 15 \]
Now we need to convert this equation into standard form, which is generally in the form \( Ax + By = C \).
Starting from:
\[ y = 12x - 15 \]
we can rearrange it:
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Subtract \( 12x \) from both sides: \[ -12x + y = -15 \]
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Multiply through by -1 to get the standard form: \[ 12x - y = 15 \]
This can also be rewritten as: \[ 12x - y = 15 \]
To compare it with the given options, let's rewrite it for clarity:
\[ -12x + y = -15 \]
Now, we'll check the options one by one:
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x − 2y = −16 (This does not match.)
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y = 12x + 8 (This is not equivalent.)
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−12x + y = 8 (This does not match.)
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2x − 2y = −16 (Dividing the whole equation by 2 gives: \( x - y = -8 \) which does not match.)
After careful comparison, it seems none of the options align with the line's correct equation in standard form.
However, if \( 12x - y = 15 \) is rewritten in a more standard format, it doesn't match.
None of the given responses accurately reflect the equation derived.
The correct response should be something like: \[ 12x - y = 15 \] or equivalent forms.
Please double-check choices provided; as of now, none match the derived line equation.