X-Intercept

The x-intercept is the name given to the intersection point of the function/line with the x-axis (abscissa) for the ordinate value y = 0 (origin).

With the equation

For any function (not necessarily affine/linear), calculating the x intercept is calculating the value for $ y = 0 $ or $ f(x) = 0 $. The value(s) obtained is/are the x-intercept(s).

Example: A curve of equation $ y=x^2-1 $, with $ y = 0 $ is solved $ x = 1 $ or $ x = -1 $, so there are 2 x-intercepts (called the roots of the polynomial)

For an equation of a line (in the 2D plane), the equation has the form $ y = a x + b $, finding $ y = 0 $ is solving $ a x + b = 0 $ so $ x = -b/a $

Example: A line of equation 2x-1 has for y-intercept 1/2

With 2 points (line only)

Knowing 2 points belonging to the line, it is possible to find its equation (see the linear equation calculator) in order to deduce the x-intercept (see above)

With the slope coefficient and 1 point (line only)

Knowing the slope coefficient of a line and one of the points belonging to it, it is possible to calculate the equation of this line (see the page on the calculation of linear equations) and therefore, with this equation, deduce the x-intercept (see above).