If f(x) = px + q then what is the value of (p + q) ?

Calculation:

Given,

The function is \(f = \{(1, 1), (2, 4), (3, 7), (4, 10)\} \), and we are also given that the function is \( f(x) = px + q \), where p and q  are constants.

Using the points f(1) = 1  and f(2) = 4 , we create the following system of equations:

- From f(1) = 1 , we have \(p(1) + q = 1 \), so p + q = 1 .......(1).

- From f(2) = 4 , we have p(2) + q = 4 , so 2p + q = 4  ..........( 2).

Subtract Equation 1 from Equation 2:

\( (2p + q) - (p + q) = 4 - 1 \)

\( p = 3 \)

Now, substitute p = 3 into Equation 1:

\( 3 + q = 1 \)

\( q = -2 \)

\( p + q = 3 + (-2) = 1 \)

∴ The value of p + q  is 1.

The correct answer is Option (3).