What are Intercepts?


An acquisition manager would like to begin a new project, the cost of which will be charged to overhead until the project becomes profitable. If he knows that the profit will increase linearly, how will he determine when the project will no longer cost the department? We can find out by plotting the graph with time as x-axis and income as y-axis. Taking time in multiples of months and cost in multiples of $10,000 the graph would look like this.




In the above graph when the time reaches the 3rd month the project starts paying for itself. The place where the line crosses the time (x) axis is the answer the manager is looking for and is called x-intercept.

Simillarly the point where the line crosses the y-axis is called y-intercept.





If we look at the above graph which represents the circle with equation x2 + y2 = 9, it cuts the x-axis at two points (x = 3 and x = -3). These points are the x-intercepts. This circle cuts the y-axis also at two points (y = 3 and y = -3). These are the y-intercepts.
From the above example it is clear that a figure may have more than one x-intercept or more than one y_intercept.