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Straight Line

 

Any equation of first degree of the form Ax + By + C = 0, where A, B, C are constants always represents a straight line (at least one out of A and B is non zero).

Slope

If θ is the angle at which a straight line is inclined to the positive direction of the x-axis, then m = tanθ, (0 < θ < 180o) is the slope of the line.

Standard Equations of the Straight Line

Slope Intercept From:

y = mx + c, where

m = slope of the line

c = y intercept

Slope Intercept From

Intercept Form:

x/a + y/b = 1

x intercept = a

y intercept = b 

Intercept Form

Slope point form

(a) One point on the straight line

(b) The gradient of the straight line i.e., the slope m of the line


Equation:

y – y1 = m(x – x1), where (x1, y1) is a point on the straight line.


Illustration:

Slope point form

Pause:

Equation of line in figure (ii) is x = 3, because x-co-ordinate of each point on the line is 3.

Equation of line in figure (iv) is y = 2, because y-co-ordinate of each point on the line is 2.

Although every line satisfied the above given basic definition, a line can be represented in many forms, some of which are given hereunder.


Two points form:

Let there be two points A(x1, y1) and B(x2, y2) in a co-ordinate plane. If any point P(x, y) lies on the line joining A and b then m = tan θ = y–y1/x–x2 = y2 – y1/x2 – x1,  (see figure given below).

Two points form

 y – y1 = y2 – y1/x2 – x1 (x – x1) which is the equation of the given line. Equation of line can also be written as

 y – y2 = y2 – y1/x2 – x1 (x – x2) or 2376_Straight line equation 1.JPG = 0.

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