If the points `A(-1,-4),B(b,c)and C(5,-1)` are collinear and 3b + c = 4, find the values of b and c.

Explanation

To find the values of \( b \) and \( c \) such that the points \( A(-1, -4) \), \( B(b, c) \), and \( C(5, -1) \) are collinear and satisfy the equation \( 3b + c = 4 \), we can follow these steps:

### Step 1: Use the Area Formula for Collinearity
The points \( A \), \( B \), and \( C \) are collinear if the area of the triangle formed by these points is zero. The area \( A \) of a triangle given by vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) can be calculated using the formula:

\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
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