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y -Intercepts

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 .

Math diagram

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 .

Math diagram

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 .

Math diagram


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