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