Final answer:
The line perpendicular to y = 3x - 8 that passes through the point (6, 1) has a slope of -1/3, resulting in the equation y = -1/3x + 3.
Step-by-step explanation:
To find the line perpendicular to y = 3x - 8 that includes the point (6, 1), we first need to determine the slope of the perpendicular line.
The original line has a slope of 3, so the slope of the perpendicular line is the negative reciprocal of that slope, which is -1/3. The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
We have the slope and a point through which the line passes, so we can use the point-slope form to find the equation:
y - 1 = -1/3(x - 6)
Distributing the slope on the right side we get:
y - 1 = -1/3x + 2
Finally, add 1 to both sides to get the equation in slope-intercept form:
y = -1/3x + 3
This is the equation of the line perpendicular to y = 3x - 8 that passes through the point (6,1).