What is the y-intercept of a line?
The y-intercept of a line is the point at which the line intersects the vertical y-axis on a Cartesian coordinate system (also known as the coordinate plane). In the coordinate plane, the x-axis is horizontal, and the y-axis is vertical. The y-intercept is the point where the line crosses or touches the y-axis.
Mathematically, the y-intercept is represented as an ordered pair (0, y), where:
- "0" represents the x-coordinate, which is always zero because the point is on the y-axis.
- "y" represents the value of the dependent variable (usually referred to as "y") at the point of intersection.
In the equation of a straight line in slope-intercept form (y = mx + b), where "m" is the slope of the line, and "b" is the y-intercept, "b" directly represents the y-coordinate of the y-intercept.
For example, if you have the equation of a line: y = 2x + 3, the y-intercept is (0, 3). This means that the line crosses the y-axis at the point (0, 3), which is 3 units above the origin.
The y-intercept is a fundamental concept in linear equations and is crucial for understanding and graphing linear functions and lines. It tells you the value of the dependent variable (y) when the independent variable (x) is zero, which is often meaningful in various real-world applications.
