What ordinate does the point C (-1; y) have, which belongs to the same straight line as the points A (-5; 2), B (-3; -1)

We have two points: A (-5; 2) and B (-3; -1).

To begin with, we write the equation of a straight line passing through these points, substituting the values of their coordinates into the formula for the straight line y = k * x + b. We obtain and solve a system of two equations with two unknowns:

2 = -5 * k + b;

-1 = -3 * k + b;

Let us subtract the first from the second equation of the system by the method of algebraic addition:

-1 – 2 = 2 * k;

2 * k = -3;

k = -3/2;

b = 2 + 5 * k = 2 – 15/2 = -11/2;

y = -3/2 * x – 11/2 – equation of a straight line.

Substitute the coordinates of the third point:

y = -3/2 * (-1) – 11/2 = 3/2 – 11/2 = -4.

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