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The x-intercept is the location on a graph where a line or a curve intersects the x-axis. The coordinate pair of any x-intercept is (x, 0) because the value of y is always 0 on the x-axis.
The y-intercept is the location on the graph where a line or curve intersects the y-axis. The coordinate pair of any y-intercept is (0, y) because the value of x is always 0 on the y-axis.
You can visually identify the x- and y-intercepts on a graph. For example, the graph below shows the height above ground of a plane during its descent in relation to time in minutes.
The y-intercept is represented by the pair (0, 30,000). This means that after 0 minutes of descent, the plane is 30,000 feet above the ground.
The x-intercept of the graph is represented by the order paired (10, 0). This means that after 10 minutes, the height of the plane is 0 feet above ground.
You can also find the x- and y-intercepts from an equation. An equation in two variables is an equation with terms involving two distinct variables. Most commonly, these variables are x and y.
EXAMPLE
The equation below represents the balance of debt during a 24-month repayment period, with the corresponding graph representation.EXAMPLE
Try finding the x- and y-intercepts for the following equation in slope-intercept form.Source: This work is adapted from Sophia author Colleen Atakpu.