Final answer:
To determine which equation is parallel to x-3y=4, we convert each option to slope-intercept form and compare slopes. Equations with the same slope of 1/3 are parallel, making options A, B, and D parallel to the given equation.
Step-by-step explanation:
The task at hand is to identify which equation is parallel to the given equation x-3y=4. To find parallel lines, we must look for equations that have the same slope. First, let's rewrite the given equation in slope-intercept form (y=mx+b), where m represents the slope:
x-3y=4 becomes 3y=x-4 and then y=(1/3)x-(4/3).
The slope of the given line is 1/3. Therefore, we need to find an equation with the same slope among the choices. By looking at each option and putting each into the slope-intercept form:
A. 2x-6y=8 becomes y=(1/3)x-(4/3).
B. 4x-12y=16 becomes y=(1/3)x-(4/3).
C. 3x+9y=12 becomes y=(-1/3)x+(4/3), which has a negative slope.
D. 5x-15y=20 becomes y=(1/3)x-(4/3).
Options A, B, and D all have the same slope as the original equation and are therefore parallel to it.
However, it is worth noting that for two equations to be parallel and distinct, they must also have different y-intercepts. Since the question does not ask for distinct parallel equations, we consider all equations with the same slope as parallel.
Thus, considering the slope alone, the correct option answers are A, B, and D.
To solve the problem completely, we conclude that the equations represented by options A, B, and D are parallel to the given equation x-3y=4.