Before we leave linear relationships, we need to consider two special kinds of linear relationships that come up in economics from time to time. To the right we show a graph of a linear relationship that is a straight, horizontal line. Such a line has a slope of zero. As we move to the right from point A to point B, Q increases from 10 to 24, but P remains unchanged at 12. So, the rise is zero, even though the run is 14. When we compute rise ÷ run for any two points on this graph the answer will always be zero since the rise will always be zero. Therefore, the Slope = 0.
This graph shows that P and Q are not related; P remains fixed at a value of 12 regardless of the value of Q.