# Slope of linear demand curve and price elasticity regions along the curve

My textbook mentions that the slope of a linear demand curve gives crucial information regarding price elasticity of demand; namely, that demand is inelastic for steeper curves and elastic for flatter ones. Later they also demarcate different regions of the curve, where the region to the northwest of the curve's midpoint shows elastic demand, and the region southeast of the midpoint inelastic demand.

I'm a little confused however on how to combine these two aspects. If you have for example a very steep linear demand curve, which is indicative of inelastic demand, but equilibrium price and quantity are in the elastic region, is demand then elastic or inelastic?

$$\frac{\partial Q}{\partial P} * \frac{P}{Q}$$
$$q = -\frac{1}{4}p + 8$$ $$q = -\frac{1}{2}p + 12$$