Write down the equation of a straight line passing through two given points A (-5; 6), B (3; -2).

We will use the fact that the equation of a straight line that passes on the coordinate plane through two points with coordinates (x1; y1) and (x2; y2) for x1 ≠ x2 and y1 ≠ y2 can be written in the following form:

(x – x1) / (x2 – x1) = (y – y1) / (y2 – y1).

Substituting the values x1 = -5, x = 3, y1 = 6 and y2 = -2 into this ratio, we get:

(x – (-5)) / (3 – (-5)) = (y – 6) / (- 2 – 6).

Simplifying this ratio, we get:

(x + 5) / (3 + 5) = (y – 6) / (- 8);

(x + 5) / 8 = (y – 6) / (- 8);

-8 * (x + 5) = 8 * (y – 6);

– (x + 5) = y – 6;

-x – 5 = y – 6;

x + y + 5 – 6 = 0;

x + y – 1 = 0.

Answer: x + y – 1 = 0.