Final answer:
The equation of line b is y = -3x + 3.
Step-by-step explanation:
The equation of line b can be found by using the fact that perpendicular lines have slopes that are negative reciprocals of each other. The slope of line a is 1/3, so the slope of line b will be -3.
Since we have the slope of line b and a point on the line (the y-intercept of line a), we can use the point-slope form of a linear equation to find the equation of line b. The point-slope form is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plugging in the values, we get the equation of line b as y - 3 = -3(x - 0), which simplifies to y - 3 = -3x or y = -3x + 3.