Page 12 - Mathematics_Form_Two

Rates and variations

Direct variations corresponding equation is y = k x , where
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Direct variation is a relationship between k is the constant of proportionality.
two variables where one variable is a For any two pairs of quantities x and y,
constant multiple of the other. In other say ( x , y ) and ( x , y ) , two equations
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2
1
2
words, if one variable increases or decreases, y = k x and y = k x are obtained. This
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FOR ONLINE READING ONLY
1
2
2
1
y
y
the other variable changes proportionally
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Mathematics for Secondary Schools This type of variation is useful for that x and y vary directly if the ratios
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implies that k = = . So, it is said
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x
x
2
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in the same direction.
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2
of the values of y to the values of x are
understanding how changes in one variable proportional.
affect another in a directly proportional
If x and y are any two quantities that are in
manner.
direct variation, then y = kx. The nature of
Engage in Activity 1.3 to explore the the equation y = kx is a straight line passing
application of direct variation in real life. through the origin, where k represents the
gradient (slope) of the line. Figure 1.1
Activity 1�3: Exploring direct shows the relation y ∝ x for k = 1.
variation in real life
y
1. Learn about direct variation from
books or from the internet.
2. Find real-life examples that
illustrate direct variations.
3. Demonstrate mathematically how
variables in the real-life scenarios
relate and use the relationship to
solve related problems. 0 x

If y is directly proportional to x, it can be

written as y ∝ x, where ∝ is a symbol
of proportionality. The corresponding
mathematical equation connecting x and y Figure 1�1: Graph of the relation y ∝ x
is formed by introducing a proportionality
constant k, and replaces ∝ with an equal From Figure 1.1, it can be observed that
sign to get, y = kx. an increase (or decrease) in the quantity

For instance, if y varies directly as x results in a proportional increase (or
the square of x , then y ∝ x and the decrease) in the quantity y, and vice versa.
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Student's Book Form Two

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