Final answer:
To find the equation of the line perpendicular to y = -10x - 8 that passes through (2, 2), calculate the negative reciprocal of the original line's slope, which is 1/10, and use the point to find the y-intercept, which is 9/5. The final equation is y = 1/10x + 9/5.
Step-by-step explanation:
The equation of line k given is y = -10x - 8. A line that is perpendicular to line k will have a slope that is the negative reciprocal of the slope of line k. Since the slope of line k is -10, the slope of the perpendicular line will be 1/10 (because -10 * 1/10 = -1). Now that we know the slope of the perpendicular line, we can use the slope-intercept form y = mx + b and the point (2, 2) through which it passes to find the y-intercept.
To find the y-intercept, plug the slope (m = 1/10) and the point (2, 2) into the slope-intercept equation:
2 = (1/10)(2) + b
2 = 1/5 + b
b = 2 - 1/5
b = 10/5 - 1/5
b = 9/5
The equation of the perpendicular line is therefore y = 1/10x + 9/5.