Without performing construction, find the coordinates of the intersection point of the graphs

Without performing construction, find the coordinates of the intersection point of the graphs of the function y = 8x and y = -2x-10.

First, let’s determine if the graphs of the functions y = 8x and y = -2x – 10 have an intersection point, or if they are parallel. The graphs of the functions y = 8x and y = -2x – 10 intersect exactly, since their slopes are different (this is the coefficient in front of x: 8 ≠ -2).
The coordinates of the intersection point are suitable for both functions, that is, their coordinates at this point are the same. Therefore, we can equate the right-hand sides of the equations:
8x = -2x – 10;

8x + 2x = -10;

10x = -10;

x = -10 / 10;

x = -1 – abscissa (x coordinate) of the intersection point.
We calculate the ordinate of the intersection point (coordinate y), substituting the found value of x into any of the functions:

y = 8x = 8 * (-1) = -8.
Answer: (-1; -8).