-- Coordinate Geometry - PureMaths 1 - RP AS & A Level Mathematics

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  • Select activity Pure Mathematics 1 1.3 Coordinate Geometry

    Pure Mathematics 1

    1.3 Coordinate Geometry
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     Video transcript

    Welcome to this short ‘insights video’ into helping learners better understand the connections between graphs and algebra. 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. Here using the two coordinates ‘x1 and y1’ and ‘x2 and y2’ a straight line is drawn.
    
    But the idea of the gradient - the steepness of the incline - the inc-’line’, is not always appreciated. 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).
    
    In this example we go ‘up’ from y equals one to five, an increase of four units. And we go ‘along’ from x equals zero to two, an increase of two units.
    
    So the gradient, how steep the slope is, is four over two, which is two.
    
    From this, learners will be able to visualise the general gradient formula, the change in y coordinates over the change in x coordinates.
    
    Often written as y2 minus y1 over x2 minus x1.
    
    Then when they have the found the gradient they can use the following formula to find the general equation of a line. Y equals m times x plus c…
    
    ...where m is the gradient and c is the value of y where the line crosses the y axis.
    
    In this case the gradient they have calculated is two and the y intercept point is one. So the equation becomes...
    
    Y equals two x plus one.
    
    A 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. 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.
    
    I hope you have found this insights video useful to help your learners visualise better the connections between graphs and algebra.
    
    Thank you.
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      Teaching Pack - 1.3 Coordinate Geometry
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      Teaching Pack - all worksheets in editable format
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  Lesson 1: Equations of a straight line
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  Lesson 2: Parallel, perpendicular or neither
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