Suppose demand is given by the equation \( Q=49-2 P \). Using the point-slope formula, what is the price elasticity of demand at a price of \( \$ 6 \) ? Include a negative sign if applicable, and round your answer to two decimal places.

To find the price elasticity of demand at a price of $6, we start with the demand equation \( Q = 49 - 2P \). First, we calculate the quantity demanded at \( P = 6 \): \[ Q = 49 - 2(6) = 49 - 12 = 37 \] Next, we need to find the slope of the demand curve, which is the change in quantity demanded divided by the change in price, represented by the coefficient of \( P \). Here, the slope is \( -2 \). Now we can use the point-slope formula for price elasticity of demand: \[ E_d = \left( \frac{dQ}{dP} \right) \cdot \left( \frac{P}{Q} \right) \] Substituting the values we have: \[ E_d = (-2) \cdot \left( \frac{6}{37} \right) \] Calculating the elasticity: \[ E_d = -2 \cdot \frac{6}{37} = -\frac{12}{37} \approx -0.32 \] Thus, the price elasticity of demand at a price of $6 is approximately \(-0.32\).