Make the equation of the straight line passing through the points A (4; -1) and B (-6; 2).

In order to form the equation of the straight line passing through the points A (4; -1) and B (-6; 2), we will compose and solve a system of equations.

For this we apply the general form of the linear equation y = kx + b;

We substitute the coordinates of the points into the equation and we get the system:

-1 = 4k + b;

2 = -6k + b.

Let us apply the substitution method to the solution.

b = -1 – 4k;

2 = -6k – 1 – 4k.

We solve the resulting equation with one variable:

2 = -6k – 1 – 4k;

-10k = 2 + 1;

-10k = 3;

k = -0.3.

System:

k = -0.3;

b = -1 – 4 * (-0.3) = -1 + 1.2 = 0.2.

y = -0.3 * x + 0.2.