Answer: y = (1/3) * x + 4
The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis. In this case, we know that the slope of the line is 1/3 and that it passes through the point (12, 16), so we can plug these values into the equation to find the y-intercept.
To do this, we first need to rewrite the point (12, 16) in the form (x, y), where x and y are the coordinates of the point. We can then substitute these values into the equation y = mx + b to find the y-intercept. This gives us the following equation:
16 = (1/3) * 12 + b
We can then solve for b by multiplying both sides of the equation by 3 and then subtracting 36 from both sides:
48 = 3 * 12 + 3b
48 = 36 + 3b
12 = 3b
Therefore, the y-intercept of the line is 12/3 = 4.
Finally, we can use the values of the slope and y-intercept to write the equation of the line in slope-intercept form. This gives us the following equation:
y = (1/3) * x + 4
This is the equation of the line with a slope of 1/3 that passes through the point (12, 16).