Final answer:
To find the equation of a line perpendicular to y=3x-6 that passes through (2,0), calculate the negative reciprocal of the given slope, which is -1/3, and use the point-slope form with the point (2,0) to obtain y = (-1/3)x + (2/3).
Step-by-step explanation:
The student is asking for the equation of a line that is perpendicular to a given line and that passes through a specific point. First, we find the negative reciprocal of the slope of the given line (3), which is -1/3. Next, using the point-slope form of a line equation (y - y1 = m(x - x1)), we plug in the given point (2, 0) and the slope -1/3 to get the equation of the perpendicular line:
y - 0 = (-1/3)(x - 2)
Simplify to get the final equation:
y = (-1/3)x + (2/3)