Why is elasticity not constant on a straight line graph? There are different zones of elasticity on a graph, but if we are to imagine a negatively sloped, straight line on a price v quantity graph, we find that elasticity differs based on where we look on the graph. Why is this the case, rather then elasticity being constant?
Theoretically, the responsiveness of quantity demanded is different at different prices. Take the equation for the elasticity of demand:
$$\epsilon_{D}=\frac{\Delta{Q}}{\Delta{P}}\frac{P}{Q}$$
The equation itself is non-constant as it depends on P and Q. Lets assume a linear demand curve with the simple form: $P(Q)=6-Q$. If we take an equal change in price, say $\Delta{P}=1$, and since the demand curve is linear in this case, we see it has a slope = $-1$ and thus the $\Delta{Q}=1$. If we have two situations where $P=5$ and $P=4$, then, to keep in accordance with our slope, lets say $Q=1$ and $Q=2$, respectively.
The two elasticities of demand for these two prices would be $\epsilon_{D}=5$ and $\epsilon_{D}=2$ for the higher and lower price respectively.

In short, the elasticity of demand is a function of the responsiveness of quantity demanded to changes in prices that depends on the current price/quantity combination.
At a higher point up the demand curve, the elasticity is higher, or demand more elastic, than at lower points.