STRAIGHT LINES AND ITS DIFFERENT FORMS.Standard 11

STRAIGHT LINES AND ITS DIFFERENT FORMS

1. STRAIGHT LINES DELSI SNEKHA A 23-EDM-05

2. STRAIGHT LINES A straight line is an endless one-dimensional figure that has no width . It is a combination of endless points joined on both sides of a point. A straight line does not have any curve in it. It can be horizontal, vertical, or slanted.

3. ANGLE OF INCLINATION The angle of inclination of a straight line is the angle, say θ, made by the line with the x-axis measured in the counterclockwise (positive) direction. SLOPE The slope or gradient of a straight line is a number that measures its “direction and steepness”.

4. COLLINEAR In a plane three or more points are said to be collinear if they lie on a same straight line. Intercepts of a Line The intercept of a line is the point at which the line crosses either the x-axis or the y-axis.

5. Different Forms of an equation of a straight line ( i ) Slope and intercept form (ii) Point and Slope form (iii) The two Point form (iv) Intercepts form (v) Normal form (vi) Parametric form

6. Slope and Intercept form Proportional linear functions can be written in the form y = mx, where m is the slope of the line. Non proportional linear functions can be written in the form, y = m x + b, b ≠ 0

7. Point - Slope form: Let m be the slope of the line and A (x 1 , y 1 ) be the given point on the line. Let P(x, y) be any point other than A on the given line. Slope of the line joining A (x 1 , y 1 ) and P(x, y) is given by m = y − y 1 /x − x 1 ⇒ y − y 1 = m(x − x 1 ).

8. Two Points form If (x 1 , y 1 ) and (x 2 , y 2 ) are any two points on the line with x 2 ≠ x1 and y 1 ≠ y 2 , then the slope is m  

9. Intercepts form: If the intercepts of a line on the x-axis and the y-axis are known, then the equation of the line can also be found using intercepts. Suppose x-intercept OA = a and y-intercept OB = b, where a and b are non-zero.  

10. Normal form: Let A and B be the intercepts made by the line. Let p be the length of the normal OP drawn from the origin to a line AB, which makes an angle α with the x-axis. x cos α + y sin α = p

11. Thank you