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C1. Ratio & proportion : direct proportion. Vocabulary The quotient of two numbers or quantities showing their relative sizes is called their ratio. The ratio of a to b is written a:b or a/b. This ratio is often expressed using the smallest possible integers. Two variable are in direct proportion to one another if they are always in the same ratio. If y is proportional to x, we write y µ x. These pairs of values of x and y display direct proportion: (1,3), (2,6), (4,12), (10,30). The ratio of y:x is always 3:1. Note that this can also be written y=3x. Values that are in direct proportion are often displayed in a table. x  2  4 10 y  8 16 40 Notice that if x is doubled, then y is doubled too. All the values fit the equation y=4x. Whenever y µ x, you will be able to find an equation of the form y=mx to fit the available information. An example y and x are in direct proportion. If y=10 when x=4, find what y is when x=12. Solution using multipliers x has been increased by a multiplier of 3, so y should be increased in the same way. So y=30 when x=12. Solution using equations The information given must fit an equation of the form y=mx. In this case 10=4m, so m=2.5, so the equation is y=2.5x. When x=12, y=2.5 × 12=30. Other examples of direct proportion x  2  4  5 y  8 32 50 In this case y is proportional to the square of x, y µx2. Written as an equation, you get y=2x2.