Note

Note ¾ If b > , then the line y=b lies above the X axis ¾ If b < , then the line y=b lies below the X axis ¾ If b = , then the line y=b is the X axis itself. ax + by + c = X X ′ ¢ Fig. . X X ′ ¢ Fig. . ( , ) ( , ) ( , ) ( , ) ( ,– ) ( ,– ) ( ,– ) ( ,– ) X X ′ ¢ Fig. . (– , ) (– , ) ( , ) (– , ) (– , ) ( , ) ( , ) ( , ) ( , ) ( , ) X X ′ ¢ Fig. . (– , b ) (– , b ) ( , b ) (– , b ) (– , b ) ( , b ) ( , b ) ( , b ) ( , b ) ( , b ) y = b . . Equation of a Straight line parallel to the Y axis Let CD be a straight line parallel to Y axis , which is at a distance ‘c’. Then x coordinate of every point on CD is ‘ c ’. The equation of CD is x = c . (fig . ) Example . Find the equation of a straight line passing through ( , ) and is (i) parallel to X axis (ii) parallel to Y axis. Solution (i) The equation of any straight line parallel to X axis is y=b . Since it passes through ( , ) , b = . Therefore, the required equation of the line is y= . (ii) The equation of any straight line parallel to Y axis is x=c Since it passes through ( , ) , c = Therefore, the required equation of the line is x= . . . Slope-Intercept Form Every straight line that is not vertical will cut the Y axis at a single point. The y coordinate of this point is called y intercept of the line. A line with slope m and y intercept c can be expressed through the equation y = mx + c We call this equation as the slope-intercept form of the equation of a line. ¾ If a line with slope m , m ≠ makes x intercept d , then the equation of the straight line is y = m ( x – d ) . ¾ y = mx represent equation of a straight line with slope m and passing through the origin. Example . Find the equation of a straight line whose (i) Slope is and y intercept is - (ii) Inclination is ° and y intercept is Solution (i) Given, Slope = , y intercept, c = − Therefore, equation of a straight line is y mx y = ⇒ (ii) Given, q = ° , y intercept, c = Slope m = tan q = ° tan = Therefore, equation of a straight line is of the form y mx Hence we get, y = ⇒ x X X ′ ¢ Fig. . ( c , ) ( c , ) ( c , ) ( c , ) ( c ,– ) x=c ( c ,– ) ( c ,– ) ( c ,– ) ( c , )