To determine which line is parallel to \( y = \frac{3}{4}x - 2 \), we need to find the slopes of the given equations. Lines that are parallel have the same slope.
The given line, \( y = \frac{3}{4}x - 2 \), has a slope of \( \frac{3}{4} \).
Now let's find the slopes of the provided equations by rewriting them in slope-intercept form (\( y = mx + b \)).
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For \( 4x - 3y = 6 \): \[ -3y = -4x + 6 \ y = \frac{4}{3}x - 2 \] (slope = \( \frac{4}{3} \))
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For \( 3x - 4y = 8 \): \[ -4y = -3x + 8 \ y = \frac{3}{4}x - 2 \] (slope = \( \frac{3}{4} \))
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For \( 3x - 4y = 12 \): \[ -4y = -3x + 12 \ y = \frac{3}{4}x - 3 \] (slope = \( \frac{3}{4} \))
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For \( 4x - 3y = 12 \): \[ -3y = -4x + 12 \ y = \frac{4}{3}x - 4 \] (slope = \( \frac{4}{3} \))
Now comparing the slopes:
- \( 4x - 3y = 6 \): slope \( \frac{4}{3} \)
- \( 3x - 4y = 8 \): slope \( \frac{3}{4} \) (PARALLEL)
- \( 3x - 4y = 12 \): slope \( \frac{3}{4} \) (PARALLEL)
- \( 4x - 3y = 12 \): slope \( \frac{4}{3} \)
The lines that are parallel to \( y = \frac{3}{4}x - 2 \) are:
- \( 3x - 4y = 8 \)
- \( 3x - 4y = 12 \)
Both of these options have a slope of \( \frac{3}{4} \).