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Lines definitions

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  • Slope
    A numerical measure of a line's steepness, found by dividing the change in y-values by the change in x-values between two points.
  • Rise
    The vertical change between two points on a line, representing the difference in y-values.
  • Run
    The horizontal change between two points on a line, representing the difference in x-values.
  • Slope-Intercept Form
    An equation format for lines, written as y = mx + b, where m is the slope and b is the y-intercept.
  • Y-Intercept
    The point where a line crosses the y-axis, found by setting x to zero in the line's equation.
  • Point-Slope Form
    A line equation format, y - y₁ = m(x - x₁), used when a slope and a specific point are known.
  • Standard Form
    A linear equation format, Ax + By + C = 0, useful for quickly finding x- and y-intercepts.
  • Parallel Lines
    Distinct lines in the same plane with identical slopes but different y-intercepts, never intersecting.
  • Perpendicular Lines
    Lines that intersect at right angles, with slopes that are negative reciprocals of each other.
  • Undefined Slope
    A situation where a line is vertical, causing division by zero in the slope formula.
  • Zero Slope
    A perfectly horizontal line, indicating no vertical change as x increases.
  • Delta
    A Greek letter (Δ) used to represent change or difference in a variable, such as Δy or Δx.
  • X-Intercept
    The point where a line crosses the x-axis, found by setting y to zero in the line's equation.
  • Ordered Pair
    A pair of numbers (x, y) representing a specific point's location on a coordinate plane.
  • Reciprocal
    A value obtained by inverting a fraction; for perpendicular slopes, the sign is also changed.