Given two points A (-1; 6) and B (9; -8). Through the middle of the segment AB draw a straight

Given two points A (-1; 6) and B (9; -8). Through the middle of the segment AB draw a straight line parallel to the straight line 2x-3y + 5 = 0.

Two points A (-1; 6) and B (9; -8) are given. Find the midpoint of the segment AB, denote this point by D:

D ((9 – 1) / 2; (6 – 8) / 2);

D (4; -1).

According to the condition of the problem, the sought line must be parallel to the line 2x – 3y + 5 = 0. This means that the first two coefficients of our line will be the same. That is:

2x – 3y + C = 0.

Let us find the coefficient C. Substitute the coordinates of point D. into this equation. We obtain:

2 * (x – 4) – 3 * (y + 1) = 0;

2x – 8 – 3y – 3 = 0;

2x – 3y – 11 = 0.

Answer: the equation of the straight line 2x – 3y – 11 = 0.