Final answer:
To find the equation of a line perpendicular to line AB and passing through point Z, determine the slope of AB and find the negative reciprocal to get the slope of the perpendicular line. Use the point-slope form of a line to find the equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to line AB and passes through point Z, we need to first determine the slope of line AB. The given equation of line AB is y = -4x - 4, which is in the form y = mx + b, where m is the slope. In this case, the slope is -4.
Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line would be 1/4.
Now that we have the slope and a point on the line (point Z), we can use the point-slope form of a line to find the equation. The equation would be y - y1 = m(x - x1), where (x1, y1) is point Z and m is the slope. Plugging in the values, we get y - y1 = (1/4)(x - x1).
However, since we don't have the coordinates of point Z, we cannot determine the exact equation of the perpendicular line. Therefore, none of the given options (A, B, C, D) can be the correct answer.