<span>Now, take a look at that definition closely. The numerator is represents the function's change in the y-direction. The denominator represents the function's change in the x-direction. This is where the idea of "rise over run" comes from. "Rise" correlates to the y-direction, and "run" correlates to the x-direction. </span>
<span>Now consider a horizontal line. It is horizontal, so that means the function does not change (i.e., remains constant) with respect to the y-direction. Mathematically speaking and considering the definition of slope defined above, no change in the y-direction means: </span>
<span>y2 - y1 = 0 </span>
<span>If the numerator is zero, then that means the fraction will equal zero, which makes the slope equal to zero. </span>