Final answer:
The equation of line k, which is perpendicular to line j given by y = -9x + 10 and passes through the point (-2, -1), is found to be y = (-1/9)x - 11/9.
Step-by-step explanation:
To find the equation of line k, which is perpendicular to line j given by the equation y = -9x + 10, and passes through the point (-2, -1), we need to determine the slope of line k. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of line k will be the negative reciprocal of the slope of line j, which is 9. Therefore, the slope of line k is -1/9.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we get:
y - (-1) = (-1/9)(x - (-2))
Simplifying this equation, we have:
y + 1 = (-1/9)x - 2/9
Subtracting 1 from both sides gives us the standard form of the equation of line k:
y = (-1/9)x - 11/9