OCR Advanced FSMQ - Additional Maths

Notice that the first equation is in the form y = mx + c , so you can immediately see that the gradient m = 2 and the intercept on the y -axis c is +1. The second form gives the equation as ax + by + c = 0. Which form you use depends on whether you are asked for a particular form in the question. You can give the equation of a straight line in either form if a form is not specified in the question. Examples 7 Find the equation of the line L , having gradient 3 and passing through the point (2, 3). Answer 7 y − y 1 = m ( x − x 1 ) where m = 3 and ( x 1 , y 1 ) = (2, 3). y − 3 = 3( x − 2) y − 3 = 3 x − 6 y = 3 x − 3 8 Find the equation of the line in the form ax + by + c = 0 that has a gradient of 2 and passes through the point (−1, 0). Answer 8 y − y 1 = m ( x − x 1 ) where m = 2 and ( x 1 , y 1 ) = (−1, 0) y − 0 = 2( x − (−1)) y = 2( x + 1) y = 2 x + 2 2 x − y + 2 = 0 6.9 Condition for two straight lines to be parallel to each other For two lines to be parallel to each other, they must have the same gradient. For example, the equation of the line that is parallel to the line y = 3 x − 2 but intersects the y -axis at y = 2 is: y = 3 x + 2 as m = 3 and c = 2 (i.e. using the equation y = mx + c ). > > >  TIP Write down the general equation for a straight line and then substitute values into it for m , x 1 and y 1 . This equation is in the form y = mx + c , where m is the gradient and c is the intercept on the y -axis. TAKE NOTE Remember to give the equation in the format asked for in the question. 2 Coordinate geometry 130