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\(x\)- and \(y\)-intercepts


The point(s) where the graph of a function intersects the \(x\)-axis is called the \(x\)-intercept(s). The point where the graph of a function intersects the \(y\)-axis is called the \(y\)-intercept. The intercepts of a function can be determined graphically and/or algebraically. For linear functions , there will be only one \(x\)-intercept and one \(y\)-intercept.

The \(x\)- and \(y\)-intercepts of a linear function are shown on the graph below.
Intercepts can be expressed in different ways. For example, the \(x\)-intercept of a function might be stated as \(4\), which means the graph of the function passes through the horizontal axis at \(x = 4\). Alternatively, the \(x\)-intercept may be expressed as an ordered pair such as \((4, 0)\). Because the \(x\)-intercept is a point on the \(x\)-axis, the \(y\)-coordinate of any \(x\)-intercept will be \(0\).

Similarly, the \(y\)-intercept of a function might be stated as \(–7\), which means the graph of the function passes through the vertical axis at \(y = –7\). Alternatively, the \(y\)-intercept may be expressed as an ordered pair such as \((0, –7)\). Because the \(y\)-intercept is a point on the \(y\)-axis, the \(x\)-coordinate of any \(y\)-intercept will be \(0\).

Knowing how to express intercepts as ordered pairs is helpful when solving problems algebraically.