This tutorial covers identifying intercepts of a line, through the exploration of:
 Defining x and yIntercepts
 Identifying Intercepts from a Graph
 Identifying Intercepts from an Equation
1. Defining x and yIntercepts
The xintercept is the location on a graph where a line or a curve intersects the xaxis. The coordinate pair of any xintercept is (x, 0) because the value of y is always 0 on the xaxis.


 xIntercept
 The location on a graph where a line or curve intersects the xaxis: (x, 0)
The yintercept is the location on the graph where a line or curve intersects the yaxis. The coordinate pair of any yintercept is (0, y) because the value of x is always 0 on the yaxis.


 yIntercept
 The location on a graph where a line or curve intersects the yaxis: (0, y)
2. Identifying Intercepts from a Graph
You can visually identify the x and yintercepts 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 yintercept 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 xintercept 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.
3. Identifying Intercepts from an Equation
You can also find the x and yintercepts 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.


 Equation in Two Variables
 An equation with terms involving two distinct variables
For example, the equation below represents the balance of debt during a 24month repayment period, with the corresponding graph representation.

You can find the xintercept by substituting 0 for y in the equation and then solving the equation for x.
Doing this, your expression becomes:

You can start to solve this equation for x by subtracting 1,080 from both sides. Next, divide by 45 on both sides, which provides x equals 24. Therefore, the xcoordinate of the xintercept is 24, and the ordered pair of the xintercept is (24, 0). This means that after 24 months, the balance of debt is $0.

Similarly, you can find the yintercept by substituting 0 for x in the equation and then solving the equation for y.
Substituting 0 for x, your equation is:

Solve the equation by multiplying 45 times 0, which equals 0. Next, add 0 and 1,080, which equals 1,080. Therefore, y equals 1,080. The ycoordinate of the yintercept is 1,080, and the ordered pair of the yintercept is (0, 1080). This means that after 0 months, the balance of debt is $1,080.


Note that for equations written as y = ax + b (slope intercept form), as in the preceding example, the yintercept can easily be defined by b, or the constant value at the end of the equation, since a times x will always be 0 when x is 0 for any value of a.


Try finding the x and yintercepts for the following equation in slope intercept form.

 To find the xintercept, you know that the value of y will be 0, so you can substitute 0 for y into the equation and solve for x. This provides 0 equals 5x minus 30. To solve for x, start by adding 30 to both sides of the equation. Divide by 5 on both sides, which simplifies to 6 is equal to x. The xintercept can be written as the ordered pair (6,0).


Notice that the y value of the ordered pair is 0, because the value of y is always 0 at the xintercept.
 Next, to find the yintercept, substitute 0 for x in the equation and solve for y. You know that the yintercept will always be the value of b in our equation, because when x is 0, a times x will always equal 0 for any value of a. However, you can complete the steps to solve the equation for y to show that this is true. Substitute 0 for x, then simplify the right side of the equation, arriving at the expression y equals 30. The yintercept can be written as the ordered pair (0, 30).


Notice that the x value of the ordered pair is 0, because the value of x is always 0 at the yintercept.
Today you learned the definition of the x and yintercepts on a graph, which is where a line or curve intersects each respective axis. You also learned how to identify the x and yintercepts from a graph, as well as how to identify the x and yintercepts from an equation.