Final answer:
The equation of a line perpendicular to y = 3/5x - 2 that passes through the point (3, -6) is y = (-5/3)x - 1.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line and passes through a given point, we first need to understand the concept of slopes of perpendicular lines. The slope of the given line, y = 3/5x - 2, is 3/5. Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the line we want to find is -5/3 (the negative reciprocal of 3/5).
Next, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line. For our line, the point is (3, -6) and the slope is -5/3. Plugging these values into the point-slope form, we get:
y - (-6) = (-5/3)(x - 3)
Simplifying this, we get:
y + 6 = (-5/3)x + 5
Subtracing 6 from both sides to get y alone gives us the final equation:
y = (-5/3)x - 1