Final answer:
The equation of a line parallel to f(x) = 3x + 1 passing through (2, -4) is y = 3x - 10, which is not among the provided options.
Step-by-step explanation:
The equation of a line parallel to f(x) = 3x + 1 that passes through the point (2, -4) can be found by using the slope of the given line. Since parallel lines have the same slope, the slope of the new line will also be 3. To find the y-intercept, we'll use the point-slope form of the equation of a line which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
To find the equation of a line that is parallel to f(x)=3x+1 and passes through the point (2, -4), we need to use the fact that parallel lines have the same slope.
The slope of the given line is 3, so the equation of the parallel line will also have a slope of 3. We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Since the line passes through the point (2, -4), we can substitute these values into the equation to solve for b. Plugging in the values, we get -4 = 3(2) + b, which gives us b = -10. Therefore, the equation of the line parallel to f(x)=3x+1 and passing through the point (2, -4) is y = 3x - 10.