Final answer:
To find the equation of a line perpendicular to y - 2 = x - 6 and passing through (–1, –6), we find the negative reciprocal of the original line's slope to be -1, and use point-slope form to arrive at the new line's equation: y = -x - 5.
Step-by-step explanation:
The question is asking for the equation of a line that is perpendicular to another given line. The given line has the equation y - 2 = x - 6, which we can rearrange into slope-intercept form as y = x - 4. This line has a slope of 1. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the new line will be -1. As the new line passes through the point (–1, –6), we can use the point-slope form y - y1 = m(x - x1) to write its equation. Substituting in the given point and the slope, we have y - (-6) = -1(x - (-1)). Simplifying this, we get the equation of the new line as y = -x - 5.