Explanation:

When two points are given, we can draw a line that connects them. This line is unique and passes through both points. Hence, the correct answer is option 'A' - only one line passes through two points.

Reasoning:

To understand why only one line can pass through two points, let's consider the definition of a line. A line is a straight path that extends infinitely in both directions. It is determined by two points on the line.

When we have two points, there is only one straight path (line) that can connect them. This is because any other path would not be straight or would not extend infinitely in both directions, thus not meeting the definition of a line.

Example:

Let's consider two points, A and B, in a coordinate plane. The coordinates of point A are (2, 3) and the coordinates of point B are (5, 7).

To find the line that passes through these two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line. The slope is given by the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the coordinates of points A and B into the formula, we get: m = (7 - 3) / (5 - 2) = 4 / 3.

Next, we can choose one of the points (let's choose point A) and substitute its coordinates into the slope-intercept form of the equation: y = mx + b.

Using point A (2, 3), we get: 3 = (4/3)(2) + b. Solving for b, we find that b = -1/3.

Finally, we can write the equation of the line that passes through points A and B: y = (4/3)x - 1/3.

Conclusion:

In conclusion, when two points are given, there is only one line that passes through them. This line is unique and can be determined using the slope-intercept form of a linear equation.

Only one straight line can pass through two points because the line will connect the two points as one as the initial and another point as the ending point...