Intercepní

Intercepní form, or intercept form, is a form of the equation of a straight line in analytic geometry. It expresses the line by its intercepts with the coordinate axes. If the line meets the x-axis at (a, 0) and the y-axis at (0, b), with a ≠ 0 and b ≠ 0, the equation is x/a + y/b = 1. Equivalently, multiplying by ab gives b x + a y = a b. The slope is -b/a, and the x- and y-intercepts are a and b, respectively.

This form is convenient for graphing when the axis intercepts are known, and for converting between forms: to slope-intercept form y = (-b/a) x + b, or to standard form ax + by = c. The intercept form is not applicable when the line passes through the origin or is parallel to one axis, because in those cases one of the intercepts is at infinity (there are no finite a or b).

Examples: A line with x-intercept 4 and y-intercept -2 has equation x/4 + y/(-2) = 1, i.e., x - 2y = 4.

Notes: In different textbooks, the same concept may be referred to as the intercept form of the equation of a line, or described in terms of its intercepts with the axes. The form highlights how a line intersects the coordinate axes and how those intercepts determine the line’s position and slope. related concepts include slope-intercept form and standard form.