Final answer:
To find the equation of the line that is perpendicular to y=(2/3)x+5 and passes through the point (5,-5), first determine the slope of the perpendicular line. Then, use the point-slope form of a line to find the equation.
Step-by-step explanation:
To find the equation of the line that is perpendicular to y=(2/3)x+5 and passes through the point (5,-5), we need to determine the slope of the perpendicular line first. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. So, the slope of the perpendicular line is -3/2. Now, we can use the point-slope form of a line to find the equation.
Using the point-slope form, y - y1 = m(x - x1) where (x1, y1) is the given point and m is the slope of the line, we substitute the values into the equation.
Therefore, the equation of the line in the form of ax + by + c = 0 is -3x - 2y + 5 = 0.