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. In other words, the y-intercept is the value of y when x is 0. For example, in the linear equation y = 2x + 3, the y-intercept is the point (0, 3) .
To find the y-intercept of a function y = f(x), you can use the following steps:
- Substitute x = 0 in the function.
- Solve for y.
- Represent the y-intercept as the point (0, y).
The y-intercept is important because it provides a starting point for a linear function and tells the value of y when x = 0. It is also used to graph functions and understand their behavior.
In summary, the y-intercept is a fundamental concept in analytic geometry, representing the point where a graph intersects the y-axis, with an x-coordinate of 0. It is essential for understanding and graphing linear functions and relations.
