x- and y- intercepts

D. x- and y- intercepts

The point where the graph of a function intersects the x-axis is called the x-intercept. 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.

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 3, which means the graph of the function passes through the horizontal axis at x = 3. Alternatively, the x-intercept may be expressed as an ordered pair such as (3, 0). Because the x-intercept is always a point on the x-axis, the y-coordinate of any x-intercept will always be 0.

Similarly, the y-intercept of a function might be stated as 5, which means the graph of the function passes through the vertical axis at y = 5. Alternatively, the y-intercept may be expressed as an ordered pair such as (0, 5). Because the y-intercept is always a point on the y-axis, the x-coordinate of any y-intercept will always be 0.

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

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