What are 5 forms of equations of lines?

Answer 1

• Standard form: ax + by + c = 0 (a, b, c constants, x and y variables)
  
• Slope intercept form: y = mx + c (m, c constants, x and y variables)
  
• Two points form: given P = (a, b) and Q = (c, d)
  (y - b)*(x - a) = (d - b)*(c - a ) (a, b, c, d constants, x and y variables)
  
• Parametric equation x = a + r*cos(t), y = b + r*sin(t) (a, b, t constants, x and y variables)
• X = A + k*B (X, A and B vectors, k scalar, X and k variables).

The standard form, parametric equation and vector form have simple analogies for 3 or more dimensions.