Formulary: Maths - Geometry - Straight Line ⁄

Straight Line ⁄

Definitions:

  • x1: x1-coordinate
  • x2: x2-coordinate
  • y1: y1-coordinate
  • y2: y2-coordinate
  • m: Slope
  • b: y-intercept
  • f:
  • y: Equation
Layer 1 x x y y 1 1 2 2

Slope Formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} \)
m = Slope
y2 = y2-coordinate
y1 = y1-coordinate
x2 = x2-coordinate
x1 = x1-coordinate


Layer 1 x x y y 1 1 2 2 b

Main Form

\( y = m \times x + b \)
y = Equation
m = Slope
b = y-intercept

\( y = \frac{y_2 - y_1}{x_2 - x_1} \times x + \left( y_2 - \frac{y_2 - y_1}{x_2 - x_1} \times x_2 \right) \)
y = Equation
y1 = y1-coordinate
y2 = y2-coordinate
x1 = x1-coordinate
x2 = x2-coordinate
y2 = y2-coordinate
y1 = y1-coordinate
y2 = y2-coordinate
x1 = x1-coordinate
x2 = x2-coordinate
x2 = x2-coordinate

\( y = m \times x + \left( y_2 - m \times x_2 \right) \)
y = Equation
m = Slope
y2 = y2-coordinate
m = Slope
x2 = x2-coordinate

\( y = m \times x + \left( y_1 - m \times x_1 \right) \)
y = Equation
m = Slope
y1 = y1-coordinate
m = Slope
x1 = x1-coordinate


Point Slope Form

\( y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} \times \left( x - x_1 \right) \)
f =
y1 = y1-coordinate
y1 = y1-coordinate
y2 = y2-coordinate
x1 = x1-coordinate
x2 = x2-coordinate
x1 = x1-coordinate