"In geometry, a line is an infinitely long object with no width, depth, or curvature."
Basic concepts of lines and slopes, including parallel and perpendicular lines.
Cartesian coordinate system: A system of identifying points on a plane using an ordered pair of numbers.
Equation of a line: A formula that describes a line's position on a coordinate plane.
Slope of a line: The measure of how steep a line is.
Point-slope form: A formula that describes a line using a given point and slope.
Slope-intercept form: A formula that describes a line using the slope and the y-intercept.
Standard form: A formula that describes a line using the x and y intercepts.
Parallel and perpendicular lines: Lines that do not intersect and lines that intersect at 90 degrees, respectively.
Collinear points: Points that lie on the same line.
Distance formula: A formula that calculates the distance between two points on a coordinate plane.
Midpoint formula: A formula that calculates the midpoint between two points on a coordinate plane.
Intercepts of a line: The points where a line intersects the x and y axes.
Vertical and horizontal lines: Lines with a slope of 0 and infinity, respectively.
Angle between two lines: The measure of the acute angle between two lines intersecting at a common point.
Perpendicular distance between a point and a line: The length of the shortest line segment connecting the point to the line that is perpendicular to the line.
Equation of a line in 3D: An equation that describes a line in a three-dimensional space.
Horizontal Line: A line that is parallel to the x-axis and has a slope of 0.
Vertical Line: A line that is parallel to the y-axis and has an undefined slope.
Parallel Lines: Lines that have the same slope but do not intersect.
Perpendicular Lines: Lines that intersect at a right angle and have slopes that are negative reciprocals of each other.
Diagonal Line: A line that is neither parallel nor perpendicular to the x-axis or y-axis.
Positive Slope: A line that rises as it moves to the right.
Negative Slope: A line that falls as it moves to the right.
Zero Slope: A line that is horizontal.
Undefined Slope: A line that is vertical.
Unit Slope: A line that rises vertically by 1 unit for every 1 unit of horizontal run.
"Thus, lines are one-dimensional objects..."
"...though they may exist embedded in two, three, or higher dimensional spaces."
"The word line may also refer to a line segment in everyday life that has two points to denote its ends (endpoints)."
"A line can be referred to by two points that lie on it..."
"...or by a single letter."
"Euclid described a line as a 'breadthless length' that 'lies evenly with respect to the points on itself'."
"...he introduced several postulates as basic unprovable properties from which he constructed all of geometry."
"Euclidean line and Euclidean geometry are terms introduced to avoid confusion with generalizations introduced since the end of the 19th century, such as non-Euclidean, projective, and affine geometry."
"Infinity length, no width, no depth, no curvature."
"...embedded in two, three, or higher dimensional spaces."
"A line segment has two points to denote its ends (endpoints)."
"A line can be referred to by two points that lie on it."
"Euclid described a line as a 'breadthless length'."
"...to construct all of geometry."
"...such as non-Euclidean, projective, and affine geometry."
"...an infinitely long object with no width, depth, or curvature."
"...though they may exist embedded in two, three, or higher dimensional spaces."
"The word line may also refer to a line segment..."
"A line can be referred to... by a single letter."