Final answer:
The equation of the line through point (-4, 0) and parallel to the y-axis is x = -4. This is because a line parallel to the y-axis is a vertical line which has an equation of the form x = k, where k is the x-coordinate of the point it passes through.
Step-by-step explanation:
The equation of a line that runs through the point (-4, 0) and is parallel to the y-axis can be determined by understanding the characteristics of vertical and horizontal lines. A line parallel to the y-axis has an undefined slope and is a vertical line. Vertical lines have equations in the form x = k, where k is the x-coordinate of all points on the line.
Since the line must pass through the point (-4, 0), we plug in -4 for k, resulting in the equation x = -4. This equation satisfies the condition of the line passing through (-4, 0) and being parallel to the y-axis.
Thus, the correct answer to the student's question is x = -4.
The equation of the line through point (-4, 0) and parallel to the y-axis is x = -4. When a line is parallel to the y-axis, the x-coordinate remains constant. In this case, since the y-axis is vertical, the line is vertical as well and the x-coordinate will always be -4, regardless of the y-coordinate