How do i find the y intercept

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

1. Find the y-intercept of the line:
   \({\text{y}}=-3{\text{x}}-9\)


2. Find the x-intercept of the line:
   \({\text{y}}=-4{\text{x}}+12\)


3. Find the y-intercept of the line:
   y − 9 = 3x


4. Find the x-intercept of the line:
   y + 12 = 2x


5. Find the y-intercept of the line:
   \({\text{x}}+6{\text{y}}=-24\)


6. Find the x-intercept of the line:
   \(5{\text{x}}+4{\text{y}}=-20\)

Background Tutorials

• X- and Y-Intercepts

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• Working with Slope-Intercept Form

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    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!

• Ordered Pairs and The Coordinate Plane

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    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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