Beginning Math and Physics for Game Programmers

Chapter 1, "Points and Lines"

Equation of a Line

The graph of an equation of the form A x + B y = C, where A and B are not both 0, is a straight line.

Slope

For any line in standard form, A x + B y = C, the slope m = “A/B.

Parallel Lines

If two lines are parallel, their slopes must be equal.

Perpendicular Lines

If two lines are perpendicular,

Equation of a Line

Slope-intercept form: y = mx + b

Point-slope form: ( y “ y ₁ ) = m( x “ x ₁ )

where ( x ₁ , y ₁ ) is a point on the line.

System of Linear Equations

A system of two linear equations in the same plane has

• Exactly one solution if the two graphs have different slopes.

• An infinite set of solutions if both graphs have the same slope and y-intercept.

• No solution if the graphs have the same slope but different y-intercepts.