Final answer:
The equation of the line parallel to y = 4x - 8 and passing through the point (3, -5) is y = 4x + 7.
Step-by-step explanation:
To find the equation of a line parallel to y = 4x - 8 and passing through the point (3, -5), we need to determine the slope of the given line and then use it to form the equation of the parallel line. The slope of the given line is 4, so the slope of the parallel line will also be 4. Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values to obtain the equation of the parallel line as y - (-5) = 4(x - 3). Simplifying, we get y = 4x + 7. Therefore, the equation of the line that is parallel to y = 4x - 8 and runs through (3, -5) is y = 4x + 7.