Question

What is the constant of proportionality in the equation y= 1/2x ?

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Answer 1

The constant of proportionality in the equation y= 1/2x is 1/2

• The given curve is of a rectangular hyperbola
• Only the positive part is considered in this curve.
• Also, the slope of the curve can be determined by comparing the coefficient of x with slope i.e 1/2
• Here y is inversely proportional to x.
• We can conclude that with an increase in x value, the value of y decreases.

Answer 2

Given :   y = (1/2)x

To Find : constant of proportionality

Solution:

Direct variation if a variable increases then other variable also increases with a constant factor   y = kx

inverse variation if a variable increases then other variable decreases with a  constant factor  xy = k

Joint variation is a relationship between atleast three variables, where one variable varies directly with all other variables.

y = kxz

Combined Variation  is a relationship between three or more variables where it is in direct variation with few variable and in inverse  variation with other variable  y = kx/z

y = (1/2)x

Here y is in direct variation with x

Hence y  ∝ x

=> y = kx     where k is constant of variation or constant of proportionality

Comparing y=kx

with y = (1/2)x

k = 1/2

Hence  the constant of proportionality in the equation   is 1/2

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