OCR Advanced FSMQ - Additional Maths

Finding the equation of line L 1 y − y 1 = m ( x − x 1 ) where m = 2 and ( x 1 , y 1 ) = (1, 2). y − 2 = 2( x − 1) y = 2 x  (or y − 2 x = 0) 10 Four straight lines have the following equations: Line 1 3 y = x + 6 Line 2 2 y = x + 10 Line 3 y = −3 x + 7 Line 4 6 y = 3 x + 12 (a) Rearrange the equations of each of these lines into the form y = mx + c and then use the equations of the lines to determine the line numbers of the two lines which are parallel to each other. (b) Determine the line numbers of the two lines which are perpendicular to each other. Answer 10 (a) Writing each equation into the form y = mx + c we obtain the following: Line 1 y = 1 3  x + 2 Line 2 y = 1 2  x + 5 Line 3 y = −3 x + 7 Line 4 y = 1 2  x + 2 Lines 2 and 4 have the same gradient ( i.e. 1 2 ) and so are parallel. (b) Lines 1 and 3 are perpendicular as the product of their gradients ( i.e. 1 3 (−3) ) is −1. TAKE NOTE Always check to see if a form for the equation of a straight line is given in the question. If the form is not specified, then either equation specified here is acceptable. 2 Coordinate geometry 132