Write down the equation of the straight line passing through the point H (2; -5) and cutting off segments of equal

Write down the equation of the straight line passing through the point H (2; -5) and cutting off segments of equal length on the coordinate axes.

Let the equation of the required straight line have the form y = k ∙ x + p. It cuts off segments of equal length d on the coordinate axes, which means that it passes through points with coordinates M (d; 0) and N (0; d). Substituting the coordinate values into the equation of the straight line, we obtain the system of equations:
0 = k ∙ d + p and d = k ∙ 0 + p, then,
d = p;
0 = k ∙ d + d;
(k + 1) ∙ d = 0;
k + 1 = 0, since d ≠ 0,
k = – 1.
In addition, the straight line passes through the point with coordinates H (2; – 5), we get:
– 5 = (- 1) ∙ 2 + p;
p = – 3, then the equation of the straight line has the form:
y = – 1 ∙ x – 3 or x + y + 3 = 0.
Answer: the equation of the straight line is x + y + 3 = 0.