To determine which lines are parallel to the line given by the equation \( y = 34x - 2 \), we need to identify the slope of this line first. The equation is in slope-intercept form \( y = mx + b \), where \( m \) represents the slope.
For the equation \( y = 34x - 2 \), the slope \( m \) is \( 34 \).
Lines are parallel if they have the same slope. Therefore, we need to rewrite the other equations in slope-intercept form (if they are not already) to find their slopes.
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For the equation \( 4x - 3y = 6 \): \[ -3y = -4x + 6 \] \[ y = \frac{4}{3}x - 2 \] (Slope = \( \frac{4}{3} \))
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For the equation \( 3x - 4y = 12 \): \[ -4y = -3x + 12 \] \[ y = \frac{3}{4}x - 3 \] (Slope = \( \frac{3}{4} \))
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For the equation \( 3x - 4y = 8 \): \[ -4y = -3x + 8 \] \[ y = \frac{3}{4}x - 2 \] (Slope = \( \frac{3}{4} \))
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For the equation \( 4x - 3y = 12 \): \[ -3y = -4x + 12 \] \[ y = \frac{4}{3}x - 4 \] (Slope = \( \frac{4}{3} \))
Now, comparing the slopes:
- Slope of \( 4x - 3y = 6 \): \( \frac{4}{3} \)
- Slope of \( 3x - 4y = 12 \): \( \frac{3}{4} \)
- Slope of \( 3x - 4y = 8 \): \( \frac{3}{4} \)
- Slope of \( 4x - 3y = 12 \): \( \frac{4}{3} \)
The lines that are parallel to \( y = 34x - 2 \) are:
- \( 4x - 3y = 6 \)
- \( 4x - 3y = 12 \)
Therefore, the correct answers are:
- \( 4x - 3y = 6 \)
- \( 4x - 3y = 12 \)
If you have to choose only one response, I would select either of the two with the same slope as the only options parallel to the original line.