Determine the point at which the line connecting the points (4; 1) and (2; 3) intersects the abscissa axis.

Decision:
1. General view of the equation of the straight line: y = k * x + b. We need to find the unknowns k and b. Since the coordinates of two points are known, we define the equation that sets the straight line. To do this, we compose a system of equations:
1 = 4k + b;
3 = 2k + b;
2. Express b from the first equation and substitute it into the second:
b = 1 – 4k;
2k + 1 – 4k = 3;
2k – 4k = 3 – 1;
-2k = 2;
k = 2 / (-2);
k = -1;
If k = -1, then b = 1 – 4k = b = 1 + 4 * 1 = 5;
3. Equation of a straight line: y = -x + 5. The straight line intersects the abscissa axis at a point whose ordinate is 0:
0 = -x + 5;
x = 5;
Answer: the point of intersection with the abscissa axis is (5; 0).