Definition
Intercept
An intercept is a point where a graph meets the x-axis or y-axis.
Continue from this idea into connected AXIO math.
Defining relationship
At an axis intercept, one coordinate has reached zero.
An intercept is a point where a graph meets a coordinate axis. At an x-intercept the y-coordinate is 0; at a y-intercept the x-coordinate is 0. A graph can have no intercepts, one intercept, or several intercepts.
At an intercept, one coordinate is zero.
What it means
An axis is like a boundary line on the coordinate plane. When a graph reaches one of those lines, the meeting point is an intercept. Because every point on the x-axis has y = 0, an x-intercept always has 0 in its y-position. The y-axis works the other way round.
Remember it
At an axis intercept, one coordinate has reached zero.
Example
For the line y = 2x − 6, set x = 0 to get the y-intercept (0, −6). Set y = 0 and solve 0 = 2x − 6, so x = 3 and the x-intercept is (3, 0).
Watch for
A point near an axis is not an intercept; the graph must actually meet the axis.
Common mix-up
The intercept is the point, such as (0, −6). People sometimes say “the intercept is −6” when they mean its non-zero coordinate.
Exact meaning
An intercept is a point where a graph meets a coordinate axis. At an x-intercept the y-coordinate is 0; at a y-intercept the x-coordinate is 0. A graph can have no intercepts, one intercept, or several intercepts.