Final answer:
To find the equation of a line perpendicular to another line, rewrite the equation of the given line in slope-intercept form. Then, determine the negative reciprocal of the slope, and use the point-slope form to find the equation of the perpendicular line.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to first determine the slope of the given line. The given line has the equation 5y - 3x = 4. We can rewrite this equation in slope-intercept form y = mx + b, where m is the slope. So we have:
5y - 3x = 4
5y = 3x + 4
y = (3/5)x + 4/5
Since the slopes of two perpendicular lines are negative reciprocals of each other, the slope of the line perpendicular to the given line is -5/3. We can then use the point-slope form y - y1 = m(x - x1) to find the equation of the perpendicular line passing through the point (5,6). So the equation becomes:
y - 6 = (-5/3)(x - 5)
Now we simplify the equation:
y - 6 = (-5/3)x + (25/3)
y = (-5/3)x + (43/3)