The coordinates of A, B, and C in the diagram are A (p, 4), B (6,1), C (9, q). What equation correctly relates p and q?

I don't see any diagram. So, I'll just wing it.

Value of q:

p, 6, 9 ⇒ there is a difference of 3. The sequence increases by 3. So, it can be assumed that the p is equal to 3. A (p, 4) ⇒ A (3,4)

Value of q:

4, 1, q ⇒ there is a difference of 3. The sequence decreases by 3. So, it can be assumed that q is equal to - 2. C (9,-2)

p q

A 3 4 ⇒ 3 + 4 = 7

B 6 1 ⇒ 6 + 1 = 7

C 9 - 2 ⇒ 9 + (-2) = 7

Notice that the sequence has an equation of p + q = 7.