But they need to check that the equation starts with ‘one y’ on the left hand side and if not, organise the equation so that it is ‘one y’ before making the substitutions. So the equation becomes.Ī common misunderstanding is that learners use the general formula and immediately assume the gradient is the coefficient of x and the intersection is the number on its own. In this case the gradient they have calculated is two and the y intercept point is one. It has two scales - one running across the plane called the x axis and. where m is the gradient and c is the value of y where the line crosses the y axis. In coordinate geometry, points are placed on the coordinate plane as shown below.
Then when they have the found the gradient they can use the following formula to find the general equation of a line. Often written as y2 minus y1 over x2 minus x1. So the gradient, how steep the slope is, is four over two, which is two.įrom this, learners will be able to visualise the general gradient formula, the change in y coordinates over the change in x coordinates. And we go ‘along’ from x equals zero to two, an increase of two units. In this example we go ‘up’ from y equals one to five, an increase of four units. Coordinate geometry is a particular branch of mathematics that gives the relation between algebra and geometry by using graphs. This can easily thought of as the amount they go ‘up’ (the y direction) over how far they have to go along (the x direction). Here using the two coordinates ‘x1 and y1’ and ‘x2 and y2’ a straight line is drawn.īut the idea of the gradient - the steepness of the incline - the inc-’line’, is not always appreciated. Many learners are very capable of plotting coordinates and drawing a straight line graph, but are sometimes lost seeing the connection between a line, and an algebraic equation. Welcome to this short ‘insights video’ into helping learners better understand the connections between graphs and algebra.
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