Final answer:
The equation of the line perpendicular to the line 6x - 18y = 36 and passing through the point (-5, 4) is y = -3x + 11.
Step-by-step explanation:
To write the equation of a line that is perpendicular to another line and goes through a given point, we will first need to determine the slope of the first line, then find the negative reciprocal of that slope to get the perpendicular slope. The equation of the given line is 6x - 18y = 36. We can convert this to the slope-intercept form, y = mx + b, to find the slope. After arranging, we get y = \( \frac{1}{3} \)x - 2, where the slope (m) is \( \frac{1}{3} \). The slope of the perpendicular line would then be the negative reciprocal, which is -3. Now, using the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is the point (-5, 4) and m is the slope -3, we get y - 4 = -3(x + 5). Simplifying, we obtain the final equation: y = -3x + 11.