The LessonThe y-intercept is the y-coordinate of the point where a line, curve or surface crosses the y-axis.
What Is the Y-Intercept of a Line?The y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis. The line below crosses the y-axis at y = 3. The y-intercept of the line is 3.
Read more about finding the y-intercept of a line
The Y-Axis Crosses the X-Axis When X = 0The y-axis crosses the x-axis when x = 0. This means that all points on the y-axis have x = 0. This is useful, because it let's us find the y-intercept of a line or a curve when we know its equation.
Finding the Y-Intercept of a Line from a Linear Equation
The y-intercept of a line can be found from the equation of a line (called a linear equation).
The slope-intercept form of a linear equation is:
In this equation, y and x are variables. m and c are letters that stand in for numbers. An example of a linear equation would be y = 2x + 1 (the m = 2 and c = 1). The y-intercept occurs when the line crosses the y-axis. On the y-axis, x = 0. The y-intercept of this equation is c.
- Finding the Y-Intercept of a Line from a Function The linear equation is an example of a function. For any value of x, it tells you y. We can find the y-intercept of any function by substituting x = 0. Read more about finding the y-intercept of a function
Lesson SlidesThe slider below gives more information about the y-intercept. Open the slider in a new tab
Positive, Zero and Negative Y-InterceptsA positive y-intercept means the line crosses the y-axis above the x-axis:
A zero y-intercept means the line crosses the y-axis at the origin:
A negative y-intercept means the line crosses the y-axis below the x-axis: