Proportional Techniques & Standard Graphs

Proportional Techniques

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STANDARD GRAPHS

Standard Graphs - linear graphs A straight line passing through the origin shows proportionality y x y  x y = k x Where k is the constant of proportionality k = rise/run

Examples of direct proportionality graph Example 1:the extension of a spring against the weight on it. extension weight Courtesy to How Science works--Graphshttp:// Science works--Graphs

Example 2:the current in a resistor against the p.d. across it. current voltage This illustrates Ohm’s Law. Examples of direct proportionality graph Courtesy to How Science works--Graphshttp:// Science works--Graphs

Standard Graph- linear graphs A straight line with a y-intercept different than zero. The relationship between y and x is linear and not proportional y  x y = m x + b Where m is the slope of the line and b is the y-intercept y x b Slope = m

A straight line graph: Example of Linear Graphs An example would be the length of a spring against the weight on it. weight length weight Courtesy to How Science works--Graphshttp:// Science works--Graphs

Standard Graphs – Power Graphs A power graph shows that y is directly proportional to x n (n> 1) y x y  x n

Power Graphs – example of Parabola A parabola is a power graph where n = 2. It shows that y is directly proportional to x 2 y x2x2 y x i.e. y  x 2 or y = kx 2 where k is the constant of proportionality

Example of a Power Graph- Parabola

Standard Graphs – Root Graphs

Example of a Root Graph- Period of a Pendulum

Standard Graphs – Inverse Graph (Hyperbola)

Standard Graphs - hyperbola P 1/V P V

Inverse Graph- Inverse Square Law g 1/R 2 g R