Final answer:
To find the equation of a line perpendicular to x - 11y = -6 and passing through (0, 3), we determine the negative reciprocal of the original slope, which is -11, and use the point-slope formula to find the new equation: y = -11x + 3.
Step-by-step explanation:
The question is about finding the equation of a line that is perpendicular to the given line x - 11y = -6 and passes through the point (0, 3). To find this, we first need to determine the slope of the given line. We rearrange it into slope-intercept form: y = mx + b where m is the slope and b is the y-intercept. The given line can be rewritten as y = (1/11)x + 6/11. Since the slopes of perpendicular lines are negative reciprocals of each other, our new line will have a slope of -11. Using the point-slope form y - y1 = m(x - x1), with point (0, 3) and slope -11, we get the equation y - 3 = -11(x - 0). Simplifying, we get y = -11x + 3 as the equation of our new line.