What is the relationship between the slope and elasticity of a demand curve?

Price elasticity of demand can be defined as the degree of responsiveness of the quantity demanded of a commodity due to change in its price. That is if price changes by 1%, then by how much %, the quantity demanded is changed.
$E_p= \frac{\%change in quantity demanded}{\%change in its price}$
On the other hand, slope of demand says 'how much will be the steepness or flatness of the curve given the price and income of the household'.
$\frac{dy}{dx}$
The price elasticity of demand and its slope are, therefore, inversely related to each other. That is, higher the elasticity, lower the slope (flatter curve) and lower the elasticity, higher the slope (steeper curve).
$\frac{dy}{dx}= \frac{1}{E_p}$


Even on a single demand curve with constant slope, there could be all the five different types of elasticities that is perfectly elastic, perfectly inelastic, elastic, inelastic, and unitary elastic.
Point at which demand curve intersects the vertical axis, elasticity is perfectly inelastic (∞), point in the middle of the curve is unitary elastic (1), point in between perfectly elastic and unitary elastic is elastic(>1) point at which demand curve intersects horizontal axis, elasticity is perfectly inelastic (0) and point in between perfectly inelastic and unitary elastic is inelastic.