x Intercept Definition

x Intercept Definition 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).