Final answer:
The line passing through (1, 4) and (3, 4) is a horizontal line with the equation y = 4. This line has a zero slope since the y-coordinates are equal. None of the given choices A-D correctly represents this horizontal line.
Step-by-step explanation:
The equation of a line that passes through two points can be found using the slope formula and then the point-slope form of the equation of a line. In this case, the two points are (1, 4) and (3, 4). First, calculate the slope (m) which is the change in y divided by the change in x. Since the y-coordinates are the same (4), the change in y is 0, resulting in a slope of 0. This indicates that we have a horizontal line. Next, we use the point-slope form, y - y1 = m(x - x1), which simplifies to y = 4, as m is 0 and one of the y-values is 4. Thus, none of the provided equation choices A-D exactly represents this line. However, from the choices given, the one that most closely represents a horizontal line with a y-intercept of 4 would be non-existent as they all imply a slope that is not zero.