Final answer:
To find the equation of the line perpendicular to y = 4/3x + 4 that passes through (4, -8), we first determine the negative reciprocal of the given line's slope. We then substitute the coordinates into the equation y = mx + b to find the y-intercept and obtain the equation y = -3/4x - 5.
Step-by-step explanation:
To find the equation of the line perpendicular to y = 4/3x + 4 that passes through the point (4, -8), we need to find the negative reciprocal of the slope of the given line. The given line has a slope of 4/3, so the negative reciprocal of 4/3 is -3/4. Now we have the slope of the new line. To find the y-intercept, we can substitute the coordinates (4, -8) into the equation y = mx + b and solve for b. Plugging in the values, we get -8 = -3/4(4) + b, which simplifies to -8 = -3 + b. Solving for b, we find b = -5. Therefore, the equation of the line perpendicular to y = 4/3x + 4 that passes through (4, -8) is y = -3/4x - 5.