To find the equation of a line with a given slope and a point it passes through, we can use the point-slope form of the equation:
y - y1 = m(x - x1),
where (x1, y1) is the given point and m is the slope.
Given that the slope (m) is -1/3 and the point it passes through is (-4, 1/3), we can substitute these values into the equation:
y - 1/3 = (-1/3)(x - (-4)),
which simplifies to:
y - 1/3 = (-1/3)(x + 4).
Now, we can multiply through by 3 to clear the fractions:
3y - 1 = -x - 4,
Rearranging the terms:
x + 3y = -3 - 1,
x + 3y = -4.
Therefore, the equation of the line with a slope of -1/3 that passes through the point (-4, 1/3) is x + 3y = -4.