If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

Options

A. p = 4, q = 5
B. p=-4,9 = 5
C. p=-4,q=-5
D. p=4,q=-5

Answer

To find the values of \( p \) and \( q \) given the function \( f(x) = px + q \) and the conditions \( f(-1) = 1 \) and \( f(2) = 13 \), we can follow these steps:

### Step 1: Set up the equations from the given conditions
Using the first condition \( f(-1) = 1 \):
\[ f(-1) = p(-1) + q = -p + q = 1 \quad \text{(Equation 1)} \]

Using the second condition \( f(2) = 13 \):
\[ f(2) = p(2) + q = 2p + q = 13 \quad \text{(Equation 2)} \]

### Step 2: Rewrite the equations
From Equation 1:
\[ -q + p = -1 \quad \Rightarrow \quad q = -p + 1 \quad \text{(Rearranging Equation 1)} \]

From Equation 2:
\[ 2p + q = 13 \quad \text{(Equation 2 remains unchanged)} \]

### Step 3: Substitute \( q \) from Equation 1 into Equation 2
Substituting \( q = -p + 1 \) into Equation 2:
\[ 2p + (-p + 1) = 13 \]
\[ 2p - p + 1 = 13 \]
\[ p + 1 = 13 \]

### Step 4: Solve for \( p \)
Subtracting 1 from both sides:
\[ p = 12 \]

### Step 5: Substitute \( p \) back to find \( q \)
Now substitute \( p = 12 \) back into the rearranged Equation 1:
\[ q = -p + 1 = -12 + 1 = -11 \]

### Final Answer
Thus, the values of \( p \) and \( q \) are:
\[ p = 12, \quad q = -11 \]