Find the general equation of the straight line passing through A (4, -2) and B (3, -1).

To compose the equation of the straight line that passes through the points with coordinates A (4; -2) and B (3; -1), we will compose and solve a system of equations.

General view of the linear equation:

y = kx + b;

We substitute in turn the coordinates of the points and solve the system of equations:

4k + b = -2;

3k + b = -1.

We solve by the addition method. System of equations:

4k + b = -2;

-3k – b = 1.

Let us add two equations of the system and write instead of the first one:

4k – 3k = 1 – 2;

b = -1 – 3k.

System:

k = -1;

b = -1 – 3 * (-1) = -1 + 3 = 2.

y = kx + b;

y = -x + 2.