Final answer:
The correct equation of the line that is perpendicular to 'y = (3/5)x - (6/5)' is 'y = -(5/3)x + (6/5)', which is option (a).
Step-by-step explanation:
To determine the equation of the line that is perpendicular to y = (3/5)x - (6/5), you first need to understand that perpendicular lines have slopes that are negative reciprocals of each other.
The slope of the given line is 3/5, so the slope of the line perpendicular to it will be -5/3. The equation of a line with slope m and y-intercept b can be written in the form y = mx + b. Therefore, the equation of the line perpendicular to y = (3/5)x - (6/5) with the y-intercept remaining the same would be y = -(5/3)x - (6/5).
However, since none of the options provided have this y-intercept, we are focusing solely on the slope to find the perpendicular line. Therefore, the correct option mentioning the correct slope and the answer to the question is a) y = -(5/3)x + (6/5).