Final answer:
To find the equation of the line parallel to y = 4x - 8 passing through the point (-8, -8), we need to determine the slope of the given line and use the point-slope form of a linear equation to write the equation of the parallel line.
Step-by-step explanation:
To find the equation of the line parallel to y = 4x - 8 passing through the point (-8, -8), we first need to determine the slope of the given line. The slope of a line in the form y = mx + b is represented by the coefficient of x, which in this case is 4. Since parallel lines have the same slope, the slope of the line we want to find is also 4. Therefore, the equation of the line parallel to y = 4x - 8 is y = 4x + b, where b is the y-intercept.
To find b, we substitute the coordinates of the given point into the equation and solve for b: -8 = 4(-8) + b. Simplifying this equation gives us -8 = -32 + b. Adding 32 to both sides gives us 24 = b. So the equation of the line parallel to y = 4x - 8 passing through the point (-8, -8) is y = 4x + 24. Therefore, the correct answer is B) y = 4x + 32.