The straight line passes through points A (0; 2) and B (3; -1). Write the equation for this straight line.

The straight line equation has the form y = kx + b. Substitute the coordinates of points A and B y into the equation of the straight line, combine the two resulting equations into the system and solve it.

A (0; 2); x = 0; y = 2; 2 = k * 0 + b;

B (3; – 1); x = 3; y = – 1; – 1 = k * 3 + b;

b = 2; 3k + b = – 1;

3k + 2 = – 1;

3k = – 1 – 2;

3k = – 3;

k = – 3: 3;

k = – 1.

Substitute the found values k = – 1 and b = 2 in the general form of the equation of the straight line, in y = kx + b:

y = – 1 * x + 2;

y = – x + 2.

Answer. y = – x + 2.