m = − coefficientof coefficientof y intercept l = − c y intercept = − constantterm coefficientof y Example . Find the slope of the straight line Solution Given slope m = − coefficientof coefficientof y = − = − Therefore, the slope of the straight line is - . Example . Find the slope of the line which is (i) parallel to (ii) perpendicular to Thinking Corner How many straight lines do you have with slope ?
Solution (i) Given straight line is ⇒ – = Slope m = − Since parallel lines have same slopes, slope of any line parallel to is . (ii) Given straight line is Slope m = − = Since product of slopes is − for perpendicular lines, slope of any line perpendicular to is − = − Example . Show that the straight lines and are parallel. Solution Slope of the straight line is m = − coefficient of coefficient of m = − Slope of the straight line is m = − = − Here, m = m That is, slopes are equal.
Hence, the two straight lines are parallel. Example . Show that the straight lines x and are perpendicular. Solution Slope of the straight line x is m = − Slope of the straight line is m = − = − Now, m m × − = − Hence, the two straight lines are perpendicular.
Example . Find the equation of a straight line which is parallel to the line and passing through the point ( , ) . Aliter a , b a , b Therefore, a Hence the lines are parallel. Aliter a = , b = − ; a , b a a b b The