Slope-intercept and intercept forms

Slope-intercept form: a line of slope m that meets the y-axis at (0, c) is y = mx + c. The number c is the y-intercept; it is negative when the line crosses below the origin.

If instead the line of slope m meets the x-axis at (d, 0), its equation is y = m(x − d).

With slope 1/2 and y-intercept −3/2 the line is y = x/2 − 3/2, or x − 2y − 3 = 0. With slope 1/2 and x-intercept 4 it is y = (x − 4)/2, or x − 2y − 4 = 0.

Intercept form: a line cutting the x-axis at (a, 0) and the y-axis at (0, b) is x/a + y/b = 1. With intercepts −3 and 2 it is x/(−3) + y/2 = 1, or 2x − 3y + 6 = 0.

Any equation Ax + By + C = 0, with A and B not both zero, is the general equation of a line. For example 3x + 2y − 12 = 0 has intercepts 4 and 6, and y = 2x + 3 crosses the x-axis at −3/2.

The triangle formed by y = m₁x + c₁, y = m₂x + c₂ and the y-axis has area (c₁ − c₂)²/(2|m₁ − m₂|). For y = x + 1, y = −x + 5 and x = 0 that is 16/4 = 4.