To find a line that is parallel to \( y = 34x - 2 \), we need to look for lines that have the same slope. The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope.
In the equation \( y = 34x - 2 \), the slope (\( m \)) is \( 34 \). Therefore, we are looking for lines that also have a slope of \( 34 \).
Let's examine the equations provided:
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3x - 4y = 12
Rearranging it into the slope-intercept form: \[ -4y = -3x + 12 \ y = \frac{3}{4}x - 3 \] (Slope is \( \frac{3}{4} \))
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4x - 3y = 12
Rearranging it into the slope-intercept form: \[ -3y = -4x + 12 \ y = \frac{4}{3}x - 4 \] (Slope is \( \frac{4}{3} \))
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3x - 4y = 8
Rearranging it into the slope-intercept form: \[ -4y = -3x + 8 \ y = \frac{3}{4}x - 2 \] (Slope is \( \frac{3}{4} \))
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4x - 3y = 6
Rearranging it into the slope-intercept form: \[ -3y = -4x + 6 \ y = \frac{4}{3}x - 2 \] (Slope is \( \frac{4}{3} \))
None of the provided equations has a slope of \( 34 \). Therefore, none of the given choices are parallel to the line \( y = 34x - 2 \).
If the answer requires a line parallel to the original, each option fails to have the required slope \( 34\).