The term "intercept" refers to the x- and y-intercepts of of a given equation. The x-intercept is the point at which a line crosses the x-axis and the y-intercept is the point at which a line crosses the y-axis. The figure below shows an example of an x-intercept (green dot) and a y-intercept (red dot).
Lines always have both an x and y-intercept unless the line is a horizontal or a vertical line. A horizontal line only has a y-intercept, while a vertical line only has an x-intercept.
Given the equation of a line, it is possible to find the x and y-intercepts by plugging in 0 for either x or y. Plugging 0 in for x then solving for y yields the y-intercept. Plugging 0 in for y then solving for x yields the x-intercept.
Find the x and y-intercepts of line 2x - 8y = 16.
Substituting 0 in for x:
2(0) - 8y = 16
-8y = 16
y = -2
The y-intercept is at (0, -2).
Substituting 0 in for y:
2x - 8(0) = 16
2x = 16
x = 8
The x-intercept is at (8, 0).
Since we know two points on the line (the intercepts) we can plot the line, as shown below.