Make an equation of a straight line passing through two points with coordinates A (4: 8) B (-6: -2).

To begin with, we write the equation of the straight line in general form:

y = kx + b.

If this straight line passes through a point with A coordinates (4; 8), then the following relation should be satisfied:

8 = 4k + b,

whence follows:

b = 8 – 4k

and the equation of the straight line takes the form:

y = kx + 8 – 4k.

If this straight line passes through a point with A coordinates (-6; -2), then the following relation should be fulfilled:

-6 = 2k + 8 – 4k,

whence follows:

2k + 4k = 8 + 6;

6k = 14;

k = 14/6 = 7/3.

Therefore, the required equation:

y = 7x / 3 + 8 – 4 * 7/3,

simplifying which, we get:

y = 7x / 3 + 8 – 28/3,

3y = 7x + 24 – 28;

7x – 3y – 4 = 0.

Answer: 7x – 3y – 4 = 0.