Final answer:
To find the slope-intercept form for the line perpendicular to y=-1/6x+4 and passing through the point (3,-2), the equation is y = 6x - 20.
Step-by-step explanation:
To find the slope-intercept form for the line perpendicular to y = -1/6x + 4 and passing through the point (3, -2), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The given line has a slope of -1/6, so the perpendicular line will have a slope of 6. Using the point-slope form of a line, we substitute the values to get y - y1 = m(x - x1). Plugging in the values, we get y - (-2) = 6(x - 3), which simplifies to y + 2 = 6x - 18. Rearranging to the slope-intercept form, the equation becomes y = 6x - 20.