Q.A demand schedule shows two points: when price is Rs. 12, quantity demanded is 40 units; when price is Rs. 8, quantity demanded is 60 units.

First find the slope from the two given points, then use one point to solve for the intercept and write the full equation; finally substitute P = 6 to find the new quantity. …

Step 1 — Find the slope using the two points $(Q_1,P_1)=(40,12)$ and $(Q_2,P_2)=(60,8)$:

Step 2 — Find the intercept ($a$) by substituting one point (say $Q=40, P=12$) into $P = a + mQ$:

Step 3 — Write the equation: $P = 20 - 0.2Q$.

Step 4 — Independent check (dual-solve), using the other point $(Q=60, P=8)$: $P = 20 - 0.2(60) = 20 - 12 = 8$. ✓ Matches, so the equation is correct.

Step 5 — Answer part (b). Substitute $P = 6$: $6 = 20 - 0.2Q \Rightarrow 0.2Q = 14 \Rightarrow Q = 70$. …

Alternatively, write the equation directly in the form $Q = c - dP$ by treating Q as a function of P from the start — swap the roles in Steps 1–2, using $\Delta Q/\Delta P$ as the slope with respect …

Using the wrong point when solving for the intercept, or making an arithmetic slip in Step 2 that then silently carries through to a wrong final answer — always re-check the fin …