The y-intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. It is the point where the graph crosses the y-axis, and the x-coordinate of this point is always 0. The y-intercept is important because it provides a starting point for a linear function and tells the value of y when x=0.
To find the y-intercept:
- Algebraically: If the linear equation is given, solve algebraically to find the y-intercept. Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y.
- Graphically: On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
For example, in the linear equation y = 6x + 8, the y-intercept is represented by the constant variable 8. This means the y-intercept is the point (0, 8) on the graph.
In summary, the y-intercept is a fundamental concept in mathematics, particularly in the study of linear functions and their graphs. It provides valuable information about the behavior of a function and its starting point on the y-axis.
