Final answer:
To find the equation of a line perpendicular to y = -x² - 6, we can determine the negative reciprocal of the slope of the given line, and use a point on the line to find the equation of the perpendicular line.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line y = -x² - 6 has a slope of -2x. The negative reciprocal of -2x is 1/2x, so the slope of the perpendicular line is 1/2x.
Now we can use the point-slope form of a line, y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. Plugging in the point (-8,1) and the slope 1/2x, we get the equation y - 1 = 1/2(x - (-8)), which simplifies to y - 1 = 1/2(x + 8).