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Straight lines chapter is one of the most crucial ones in Mathematics for JEE, BITSAT and other competitive exams. The concept of Straight lines is not only used in Mathematics, but also in Physics and Chemistry. Straight lines is mainly based on Co-ordinate geometry without which the whole Conics problems cannot be cracked.

Let us see the main concepts which should be learnt in the chapter of straight lines:

  1. Shifting of origin.
  2. Slope of a line and angle between two lines.
  3. Various forms of equation of a line: Parallel to axis, Point slope form, Slope intercept form, Two point form, Slope intercept form, Intercept form, Normal form, General equation of line, Distance of a point from a line, Foot of perpendicular, Distance between two parallel lines and Family of lines passing through point of intersection of two lines.

Many of the results, proofs in Geometry can be easily obtained by using basic concepts of Straight lines. Straight lines chapter serves as a backbone to the total Conics topic. In fact, each and every chapter will be using the concepts of straight lines in some way or the other. It plays a major role in Physics contributing in Kinematics, Thermodynamics, Optics and many more. Chemistry also uses the concept of extrapolation by which they estimate the values which are not possible through experiments.

Straight lines is one of those amazing topics that opens students minds to the various possibilities of finding the shortest approaches to tackle a problem by using numerous concepts. Concepts of straight lines are used in many different situations. They don’t have boundaries and keep on mingling with other concepts to make the task even more interesting and challenging.

Let us see an illustration of Straight lines:

Linear equations all look like this y= mx + b.

where ‘m’ is your rate of change. Ask yourself, when that x thing goes up by 1, how much does y go up (or down)? This will be your m.

‘b’ is your constant. This is the initial value of ‘y’. The value of ‘y’ when ‘x’ is 0.

Finally, ‘y’ is the thing that depends on ‘x’.

Oh right, examples:

1.) I buy a printer for $100 and the ink cartridges cost $25 each. What is the relationship between ink cartridges and total cost?

total cost = 25(cartridges I buy) + 100 or y = 25x + 100

In the real world, Straight lines concepts can be used in many situations: We can use them for maximizing the profits obtained by sellers, for statistics purposes and predicting the values which occur at later stages which are not obtained through experiments. Even in Economics, the demand and supply relations are based on the concepts of Straight lines. The Zero order reactions in Chemistry are also related to Straight line. 

In conclusion one should be thorough with the concepts of straight lines in order to approach problems in a short way. Many exams involve these concepts if one is good at them it will be perk for him/her for getting good marks.

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