Line Intercept Form Calculator (x/a + y/b = 1)

Enter the x-intercept a and y-intercept b to find the slope, equation, general form, distance from the origin, and intercept triangle area of a line, with a coordinate diagram.

Input

Enter the x-intercept a and y-intercept b to compute the slope, general form, and more for the line x/a + y/b = 1.

x-intercept a

y-intercept b

Result

Slope

-0.75

Equation

x/4 + y/3 = 1

Distance from origin

2.4

Triangle area

General form 3x + 4y + -12 = 0

The slope and distance are based on the units of the intercepts you entered.

How it works

A line in intercept form is written as x/a + y/b = 1, where a is the x-intercept and b is the y-intercept. Both a and b must be nonzero.
Multiplying both sides by a b gives b x + a y = a b, which rearranges into the general form A x + B y + C = 0 with A = b, B = a, and C = -a b.
The slope is m = -b / a.
The distance from the origin to the line A x + B y + C = 0 is the absolute value of C divided by the square root of A squared plus B squared.
The triangle bounded by the x-intercept, the y-intercept, and the origin has area equal to the absolute value of a b divided by 2.

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