The y -intercept of a graph is the point where the graph crosses the y -axis. (Because a function must pass the vertical line test , a function can have at most one y -intercept . )
The y -intercept is often referred to with just the y -value. For example, we say that the y -intercept of the line shown in the graph below is 3.5 .
When the equation of a line is written in slope-intercept form ( y = m x + b ), the y -intercept b can be read immediately from the equation.
Example 1:
The graph of y = 3 4 x − 2 has its y -intercept at − 2 .
Similarly, for a quadratic equation written in standard form y = a x 2 + b x + c , the y -intercept is c .
Example 2:
The graph of y = − x 2 − x + 3 has its y -intercept at 3 .
The Algebra of Lines:
When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.
To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.
When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.
Video Source (08:37 mins) | Transcript
To find y-intercept: set x = 0 and solve for y. The point will be (0, y).
To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).
Additional Resources
- Khan Academy: Introduction to Intercepts (06:32 mins, Transcript)
- Khan Academy: X-intercept of a Line (01:42 mins, Transcript)
- Khan Academy: Intercepts from an Equation (04:07 mins, Transcript)
Practice Problems
- Find the y-intercept of the line:
\({\text{y}}=-3{\text{x}}-9\) - Find the x-intercept of the line:
\({\text{y}}=-4{\text{x}}+12\) - Find the y-intercept of the line:
y − 9 = 3x - Find the x-intercept of the line:
y + 12 = 2x - Find the y-intercept of the line:
\({\text{x}}+6{\text{y}}=-24\) - Find the x-intercept of the line:
\(5{\text{x}}+4{\text{y}}=-20\)
Background Tutorials
X- and Y-Intercepts
Working with Slope-Intercept Form
What's Slope-Intercept Form of a Linear Equation?
When you're learning about linear equations, you're bound to run into the point-slope form of a line. This form is quite useful in creating an equation of a line if you're given the slope and a point on the line. Watch this tutorial, and learn about the point-slope form of a line!
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Ordered Pairs and The Coordinate Plane
What is the X-Coordinate?
Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the x-coordinate in an ordered pair!
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What is the Y-Axis?
To graph a function or plot an ordered pair, you need to use a coordinate plane, so you should learn all about it! In this tutorial, you'll learn about the y-axis and see where it's located in the coordinate plane.
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