1.3.2—Line equation forms

Use y=mx+c for gradient/intercept, y−y₁=m(x−x₁) for a known point and gradient, and ax+by+c=0 for intersections, distances or a normal-vector description.

Convert between forms carefully and keep coefficients proportional when comparing the same line. For a line through two points, calculate its gradient before choosing the form.

2x−3y+6=0 becomes y=(2/3)x+2, revealing gradient 2/3 and y-intercept 2.

Multiplying all coefficients by a non-zero constant gives the same line; changing only one coefficient changes its geometry.