Line m passes through the points (–5, 9) and (–1, 9).

Line M is a horizontal line with a slope of zero

Let me tell you why, first the y intercepts are not changing, the x intercepts are just changing which means that the line will be horizontal. You can also prove this by actually graphing the points and connecting the dots.

Two, a horizontal line always has a slope of zero, slope is rise over run, when rise = 0, no matter what the run is the slope will be zero. 
For example 0/9 = 0, 0/1 = 0.