How do you find intercepts?


Example: Let us consider the graph for the equation 4x2 + 9y2 = 36.




In the above graph we can observe that whenever the ellipse cuts the x-axis, the y-coordinate becomes zero. Therefore, to find the x-intercept we just need to set y equal to zero in the equation of the curve.

Solution: So, to find the x_intercept for the equation 4x2 + 9y2 = 36, we set y = 0 and obtain,

4x2 = 36
x2 = 9
x = +3 and -3

Similarly we can find y-intercepts by setting x equal to zero in the equation and solving for y.

Let us find y_intercept for the same equation 4x2 + 9y2 = 36. Setting x = 0 yields


9y2 = 36
y2 = 4
y = +2 and -2

Example: Consider the equation x - 2y = 1.The x and y intercepts are obtained by making y and x equal to zero, respectively.

Solution: The x-intercept is x = 1 and the y-intercept is y = -1/2.

Would you like to see a graphical representation?
Graphical interactive workbench

Try this problem. Find the intercepts for equation y = x 3 - x.