The point on a graph where the curve of a function crosses the x – axis is known as its x – intercept. The value of y – coordinate is zero at the point where the graph intersects the x – axis. To find the x – intercept of an equation, we put the value of y as zero in the equation and solve the equation to find the corresponding value of x.
Example 1: Find the x – intercept for the following equation of a line:
3x – 5y = 12.
Solution: In order to find the x – intercept we need to put the value of y = 0 in the equation and solve the equation to find the corresponding value of x.
3x – 5 (0) = 12
3x – 0 = 12
3x = 12
x = 4
Therefore the x – intercept for the above equation of line is (4, 0)
Example 2: Find the x – intercept for the function y = x2 – x – 6
Solution: For finding the x – intercept of the above function, the value of y is taken as 0. As a result we get an equation with terms having variables x and x2 on one side and zero on the other side. We need to solve this equation to get the corresponding value of x.
x2 – x – 6 = 0
x2 – 3x + 2x – 6 = 0
x( x- 3) + 2(x-3) = 0
(x+2) (x-3) = 0
x +2 = 0 or x – 3 = 0
x = - 2 x = 3
Thus the x – intercepts for the above function are (-2, 0) and (3, 0).