Answer:
To find the equation of the line parallel to 3y = 6x -1 passing through the point (1, -4), we need to first determine the slope of the given line. We can rearrange the given equation into slope-intercept form (y = mx + b) to find its slope:
3y = 6x - 1
y = 2x - 1/3
The slope of the given line is 2.
Since we want to find the equation of a line parallel to this line, the slope of the new line must also be 2. We can use the point-slope form of the equation of a line to find the equation of the new line:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is the given point that the line passes through.
Substituting m = 2 and (x1, y1) = (1, -4), we get:
y - (-4) = 2(x - 1)
Simplifying, we get:
y + 4 = 2x - 2
Subtracting 4 from both sides, we get:
y = 2x - 6
Therefore, the equation of the line parallel to 3y = 6x -1 passing through the point (1, -4) is y = 2x - 6.