Straight Line

A straight line is a curve such that every point on the line segment joining any two points on it lies on it.

 If a point moves on a plane in a given direction then its locus is called a straight line and the equation of its locus is called the equation of the straight line.
Every first degree equation in x, y represents a straight line.
When we say that a first degree equation in x, y i.e., ax + by + c = 0 represents a line, it means that all points (x, y) satisfying ax + by + c = 0 lies along a line. Thus a line is also defined as the locus of a point satisfying the condition ax + by + c = 0 where a, b, c are constants.

We can have different forms of the equation of a straight line by assigning the direction of the moving point in various methods. However, these different forms of equation of a line are not independent i.e., one form of equation of a line can be reduce to other form. It follows from the above discussion that ax + by + c = 0 is the general equation of a line.

It should be noted that there are only two unknowns in the equation of a straight line because equation of every straight line can be put in the form ax + by + c = 0 where a, b are two unknowns. Note that x, y are not unknowns. In fact these are the coordinates of any point on the line and are known as the current coordinates. Thus, to determine a line we will need two conditions to determine the two unknowns. In the further discussion on straight line we will find that whenever it will be asked to find a straight line there will always be two conditions connecting the two unknowns.

● The Straight Line

• Straight Line
• Slope of a Straight Line
• Slope of a Line through Two Given Points
• Collinearity of Three Points
• Equation of a Line Parallel to x-axis
• Equation of a Line Parallel to y-axis
• Slope-intercept Form
• Point-slope Form
• Straight line in Two-point Form
• Straight Line in Intercept Form
• Straight Line in Normal Form
• General Form into Slope-intercept Form
• General Form into Intercept Form
• General Form into Normal Form
  
• Point of Intersection of Two Lines
  
• Concurrency of Three Lines
• Angle between Two Straight Lines
• Condition of Parallelism of Lines
• Equation of a Line Parallel to a Line
• Condition of Perpendicularity of Two Lines
• Equation of a Line Perpendicular to a Line
• Identical Straight Lines
• Position of a Point Relative to a Line
• Distance of a Point from a Straight Line
• Equations of the Bisectors of the Angles between Two Straight Lines
• Bisector of the Angle which Contains the Origin
• Straight Line Formulae
• Problems on Straight Lines
• Word Problems on Straight Lines
• Problems on Slope and Intercept

11 and 12 Grade Math

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