The straight line y = kx + b passes through points A (-1; 3) and B (2; -1). Write the equation for this straight line.

We know that the line y = kx + b passes through the points with coordinates A (- 1; 3) and B (2; – 1).

Based on this, we will compose and solve a system of linear equations.

3 = – 1 * k + b;

– 1 = 2k + b.

We will solve the system by the substitution method. Let us express the variable b from the first equation of the system.

b = 3 + k;

2k + b = – 1.

Substitute the expression 3 + k into the second equation instead of b and solve the resulting linear equation.

b = 3 + k;

2k + 3 + k = – 1.

3k = – 1 – 3;

3k = – 4;

k = – 4/3 = – 1 1/3.

System:

b = 3 + (- 1 1/3) = 5/3 = 1 2/3;

k = – 1 1/3.

Let’s write the equation of a straight line passing through the given points:

y = – 1 1 / 3x + 1 2/3.

Answer: y = – 1 1 / 3x + 1 2/3.