Write the equation of a line in slope intercept form perpendicular to y= -3x+4 passing through the point (-6,6)

1. Find the slope of the given line, which is -3.
2. The slope of the perpendicular line is the negative reciprocal. So, the new slope is \frac{1}{3}.
3. Use the point-slope form (y - y_1 = m(x - x_1)) with the point $(-6, 6)$ and slope \frac{1}{3}.
y - 6 = \frac{1}{3}(x + 6)
4. Distribute the slope:
y - 6 = \frac{1}{3}x + 2
5. Add 6 to both sides to get the slope-intercept form:
y = \frac{1}{3}x + 8

Final answer: y = \frac{1}{3}x + 8