Finding the x- and y-intercepts of a linear equation can be done in several ways, but one of the easiest is the substitution method. By substituting 0 for the values of x and y in the equation, each intercept can be located without having to graph the equation.
The x- and y-intercepts mark the two points at which the line crosses the respective axis, and using the substitution method is the most straightforward way of finding these points. Other methods exist, depending on what information is known or easily derived. If the equation is in slope-intercept form of y = mx + b, then b is the y-intercept. If two points are known and a graph is handy, it is possible to simply draw the line through the points and trace it to the x-axis and y-axis, noting where the line crosses and checking the values in the equation. When the values of x and y are plugged into the linear equation, it should hold true for all points on the line.
If only the y-intercept is required, convert the equation to slope-intercept form. If both points are needed, it's best to put it in standard form ax + by = c. This decreases the likelihood of awkward fractions.