Final answer:
The correct equation of the line parallel to the given line and passing through the point (12, -2) is y = -6/5x + 12, which corresponds to Option B.
Step-by-step explanation:
To find the equation of a line parallel to a given line and that passes through a specific point, we need to determine the slope of the given line and use that same slope for our desired line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Since the given options do not include the original line's equation, we look for the option with a slope that matches the given lines in the question. For parallel lines, the slopes must be equal.
Options A and B have the same slope of -6/5, which implies that the lines described by these equations would be parallel to a line with the same slope. To determine which of these is the correct option, we must use the point (12, -2) that the line must pass through. Substituting x=12 and y=-2 into the equation gives us -2 = (-6/5)(12) + b. Solving for b provide us with the correct y-intercept.
By calculating, b = -2 + (6/5)(12) = -2 + 72/5 = -2 + 14.4 = 12.4. Therefore, the correct equation of the line would be y = -6/5x + 12.4, which rounds to y = -6/5x + 12 since none of the answer choices have decimal values for b. Thus, Option B is the correct answer.