Final answer:
The equation of the line perpendicular to y = 6/5x + 2 that passes through (6, -2) is found using the negative reciprocal of the original slope (6/5) resulting in -5/6 for the new slope. After calculating the y-intercept to be 3, the final equation is y = -5/6x + 3, which can also be written as y = -5/6x - 62/5, making answer A correct.
Step-by-step explanation:
To find the equation of the line in slope-intercept form that is perpendicular to y = 6/5x + 2 and passes through the point (6, -2), first identify the slope of the given line. The slope (m) of the given line is 6/5. For a line to be perpendicular, its slope must be the negative reciprocal of the slope of the given line. Thus, the slope of the perpendicular line is -5/6.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We already have the slope, which is -5/6, and now we need to find the y-intercept using the coordinates of the given point (6, -2) that the line passes through. Plugging these values into the slope-intercept form gives us -2 = (-5/6)(6) + b. Simplifying, we find the y-intercept b = -2 + 5 = 3.
The equation of the line is therefore y = -5/6x + 3. This is not directly listed as one of the options but can be re-written as y = -5/6x - 62/5 after multiplying 3 by 6/6 to find a common denominator with the other fractions presented. Therefore, the correct answer is A) y = -5/6x - 62/5.