Final answer:
To find the equation of a line perpendicular to another line, we need to determine the slope of the original line and then find the negative reciprocal of that slope. The equation of the line that passes through the point (5,6) and is perpendicular to the line 5x - 3y = 0 is 3x + 5y = 33.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to determine the slope of the original line and then find the negative reciprocal of that slope. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope. In the given line, 5x - 3y = 0, we rearrange it to get y = (5/3)x. The slope of this line is 5/3, so the slope of the line perpendicular to it is -3/5. Now that we have the slope and the point (5,6) that the line passes through, we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y -6 = (-3/5)(x - 5). Simplifying the equation, we get y = (-3/5)x + (33/5). Therefore, the equation of the line that passes through the point (5,6) and is perpendicular to the line 5x - 3y = 0 is (3x + 5y = 33).