
Equation of a linePage navigation:
Line is an endless line, which forms the shortest path between any of two its points.
Equation of a line on planeGeneral form of a line equationAny equation of a line on plane can by written in the general form A x + B y + C = 0 where A and B are not both equal to zero. Slope intercept form of a line equationThe general equation of a line when B ≠ 0 can be reduced to the next form y = k x + b where k is the slope of the line and b is the yintercept. Slope of the line is equal to the tangent of the angle between this line and the positive direction of the xaxis. The ycoordinate is the location where line crosses the yaxis. Equation of the line passing through two different points on planeIf the line passes through two points A(x_{1}, y_{1}) and B(x_{2}, y_{2}), such that x_{1} ≠ x_{2} and y_{1} ≠ y_{2}, then equation of line can be found using the following formula
Parametric equations of a line on planeParametric equation of the line can be written as
where (x_{0}, y_{0}) is coordinates of a point that lying on a line, {l, m}  координаты направляющего вектора прямой. Canonical equation of a line on planeIf you know the coordinates of the point A(x_{0}, y_{0}) If you know the coordinates of the point n = {l; m}, then the equation of the line can be written in the canonical form using the following formula
Example 1. Find the equation of a line passing through two points A(1, 7) and B(2,3). Solution. We use the formula for the equation of a straight line passing through two points
From this equation, we express y in terms of x
y  7 = 4(x  1) y = 4x + 11 Equation of a line in spaceEquation of the line passing through two different points in spaceIf the line passes through two points A(x_{1}, y_{1}, z_{1}) and B(x_{2}, y_{2}, z_{2}), such that x_{1} ≠ x_{2}, y_{1} ≠ y_{2} and z_{1} ≠ z_{2}, then equation of line can be found using the following formula
Parametric equations of a line in spaceParametric equation of the line can be written as
where (x_{0}, y_{0}, z_{0}) is coordinates of a point that lying on a line, {l; m; n} is coordinates of the direction vector of line. Canonical equation of a line in spaceIf you know the coordinates of the point A(x_{0}, y_{0}, z_{0}) that lies on the line and the direction vector of the line n = {l; m; n}, then the equation of the line can be written in the canonical form using the following formula.
Straight line as crossings of two planesIf the line is the intersection of two planes, then the equation of line can be found as the solution of the following system of equations
on condition that there has not been equality
Analytic geometry: Introduction and contentsDistance between two pointsMidpoint. Coordinates of midpointEquation of a lineEquation of a planeDistance from point to planeDistance between two planesDistance from a point to a line  2DimensionalDistance from a point to a line  3DimensionalAngle between two planesAngle between line and plane
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