When we say that a line passes through a point, we mean that the specific coordinates of that point satisfy the equation of the line. In simpler terms, if you have a line represented by an equation in a coordinate system, and you have a point with coordinates (x, y), you can substitute these values into the equation of the line.
If the equation holds true after the substitution, it means the line intersects the point. For example, consider the line represented by the equation y = 2x + 3. If we have the point (1, 5), we can substitute x = 1 into the equation:
y = 2(1) + 3
y = 2 + 3
y = 5
Since the calculated y-value matches the y-coordinate of the point, we can conclude that the line does indeed pass through the point (1, 5).
In a geometric sense, when a line passes through a point, it means that the point lies on the line, and you can visualize this by plotting both the line and the point on a graph. Understanding this concept is crucial when studying geometry, algebra, and how these elements interact in mathematical problems.