Final answer:
The correct equation of the line through the point (8, -5) that is perpendicular to the given line y = 4/3 x + 7 is y = -3/4 x - 11, which corresponds to Option A.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, you first need to understand the relationship between their slopes. The given equation y = 4/3 x + 7 has a slope of 4/3. For a line to be perpendicular, its slope must be the negative reciprocal of this slope, which would be -3/4.
With the slope of the perpendicular line established as -3/4, you would now use the point given, which is (8, -5), to find the y-intercept (b) of the new line using the point-slope form of a linear equation, which is y - y1 = m(x - x1). Plugging in the values, you get y + 5 = -3/4(x - 8). Simplifying this equation, you multiply out the right side and then isolate y to get the y-intercept. After simplifying, you obtain the equation y = -3/4x - 11, which matches option A from the provided choices. Therefore, the equation of the line through the point (8, -5) and perpendicular to y = 4/3x + 7 is Option A: y = -3/4x - 11.