Final answer:
The line parallel to 3x - 4y = 12 that passes through the point (8, -2) has the equation 3x - 4y = 32. However, none of the provided options match this equation, indicating an error in the question.
Step-by-step explanation:
To find the equation of a line parallel to another and passing through a specific point, we should keep the slope the same and find the new y-intercept. The given equation 3x - 4y = 12 has the slope represented by the coefficients of x and y. Since parallel lines have the same slope, our new equation will also have the form 3x - 4y = b. To find the value of 'b', we use the point (8, -2) through which the line passes.
Substitute x = 8 and y = -2 in the equation 3x - 4y to get:
3(8) - 4(-2) = 24 + 8 = 32.
Therefore, the new equation is 3x - 4y = 32, but this option is not listed among the choices provided. We can see that the equation 3x - 4y = -12 (option c) is not correct as it does not match our calculation. Hence, there seems to be a mistake as none of the provided options match the correct equation.