# $y$ -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 $3.5$ .

When the equation of a line is written in slope-intercept form ( $y=mx+b$ ), the $y$ -intercept $b$ can be read immediately from the equation.

**
Example 1:
**

The graph of $y=\frac{3}{4}x-2$ has its $y$ -intercept at $-2$ .

Similarly, for a quadratic equation written in standard form $y=a{x}^{2}+bx+c$ , the $y$ -intercept is $c$ .

**
Example 2:
**

The graph of $y=-{x}^{2}-x+3$ has its $y$ -intercept at $3$ .

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