Final answer:
The line parallel to the equation 3y + 4X = -6 is Option B: 3Y = -4X + 0 because after rearranging, both have the identical slope of -4/3.
Step-by-step explanation:
The student's question is about determining which of the given lines are parallel to the line represented by the equation 3y + 4X = -6. To answer this, we need to find an equation with a slope that is equal to the slope of the given line. First, we rewrite the given equation in slope-intercept form (y = mx + b), which gives us y = (-4/3)x - 2. The slope here is -4/3. Now we examine the given options:
- Option A: Y = 12/9 X-1 has a slope of 12/9, which simplifies to 4/3. This is not equal to the slope of the original line, so it is not parallel.
- Option B: 3Y = -4X + 0 can be rearranged to Y = (-4/3)X, which indeed has a slope of -4/3. This line is parallel to the original line.
- Option C: -2Y = 5X-8 has a slope of -5/2 when solved for Y, which is not equal to -4/3, so it is not parallel.
- Option D: -4X = -4Y + 1 rearranges to Y = X - 1/4, which has a slope of 1, so this line is not parallel to the original line either.
Thus, the line that is parallel to 3y + 4X = -6 is Option B: 3Y = -4X + 0.