Final answer:
To find the equation of line k, which is perpendicular to line j and passes through a given point, we can use the point-slope form of a linear equation. The equation of line k is y + 1 = (1/9)(x + 2).
Step-by-step explanation:
To find the equation of line k, which is perpendicular to line j, we need to find the slope of line j. We can see from the given equation for line j, y = -9x + 10, that the slope is -9. The slope of any line perpendicular to line j will be the negative reciprocal of -9, which is 1/9.
Since line k passes through the point (-2, -1), we can use the point-slope form of a linear equation to find its equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Substituting the values -2, -1, and 1/9 into the point-slope form, we get the equation of line k as y + 1 = (1/9)(x + 2).