Final answer:
The equation connecting Q and P is Q = 2P + 4 by solving the system of equations derived from the given points and the linear relationship.
Therefore, the correct answer is: option c) Q = 2P + 4
Step-by-step explanation:
The question involves finding the equation of a linear relationship between two variables, P and Q, given two points on the line.
Using the given points, (P= a, Q=6) and (P= 10, Q=24), we can find the values of a and C in the linear equation Q = aP + C.
First, we can substitute the first point into the equation, giving us 6 = a * a + C.
Next, we substitute the second point, yielding 24 = 10a + C. Solving these two equations simultaneously, we can find the values of a and C.
From the first equation, we can express C as C = 6 - a2.
Substituting this into the second equation we get 24 = 10a + 6 - a2.
Simplifying, we have a2 - 10a + 18 = 0.
This quadratic equation factors to (a - 2)(a - 9) = 0, meaning a is either 2 or 9.
However, if a were 9, the equation Q = 6 when P = a (P = 9) would not be true. So, a must be 2.
Now that we know a = 2, we can substitute back into C = 6 - a2 to find C.
C = 6 - 22
= 6 - 4
= 2.
This gives us the final equation, Q = 2P + 4, which corresponds to option (c).