N6 Ratio and proportionppt IslandMaths10N6比和prportionppt islandmaths10.pptVIP

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N6 Ratio and proportionppt IslandMaths10N6比和prportionppt islandmaths10.ppt

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N6 Ratio and proportionppt IslandMaths10N6比和prportionppt islandmaths10

* * Note that here we have worked out k for diameters given in mm. This is fine, so long as we continue to calculate using diameters in millimetres. * * Ask pupils to fill in the missing values in the table by finding the constant of proportionality for the given relationship or otherwise. * * Discuss what type of proportion is shown by each graph. When n = 1, y is directly proportional to x. When n 1, y is directly proportional to x2, x3 or any other positive power of x. When 0 n 1, y is directly proportional to any nth root of x. When n 0, y is inversely proportional to x or any power of x. * Vary the value of k and note the basic properties of each graph. When y ? x, It is a straight line that passes through the origin. As x increases by a fixed amount, y increases by a fixed amount. The value of k, the constant of proportionality is given by the gradient of the graph. When y ? 1/x, It is a curved line that does not pass through the origin. It never touches the x- or y-axis. As x increases by a fixed amount, y decreases in decreasing amounts. The greater the value of k, the steeper the graph. When y ? x2, It is a curved line that passes through the origin. As x increases by a fixed amount, y increases by increasing amounts. This can be investigated by using the pen tool to show how many units y increases by for each unit in the x direction. The greater the value of k, the steeper the graph. Explain that if y varies directly with any power of x greater than 1 a similar shaped graph will be produced. Compare this graph with graphs then show repeated proportional change by an amount greater than 1 (that is, those showing exponential increase). See the graphs of exponential functions in A9 Graphs of non-linear functions. When y ? √x, It is a curved line that passes through the origin. As x increases by a fixed amount, y increases by decreasing amounts. This can be investigated by using the pen tool to show how many units y increases by for each unit in