Explain proportional values

Explain proportional values O Fig. 1.8 2. Proportional values. If variables y and x are direct pro- Tortional. then the functional dependence between them represented by the equation: where k is a constant a factor of proportionality. A graph of a direct proportionality is a straight line, Ding through an origin of coordinates and forming with n x-axis an angle a, a tangent of which is equal to k: -n a = k. Therefore, a factor of proportionality is called I so a slope. These are shown in three graphs with k = 1/3, = 1 and k --3 on Fig.1.9 k=—3 a O x

A p r o p o r t i o n a l f u n c t i o n i s d e f i n e d a s f : ℝ \to ℝ f (x) = k x, k i s c a l l e d f a c t o r o f p r o p o r t i o n a l i t y o r p r o p o r t i o n a l i t y c o n s \tan t y = k x a c t u a l l y r e s p r e s e n t a s t r a i g h t l i n e p a s \sin g t h o r u g h o r i g i o n k i s c a l l e d t h e s l o p e o f t h e l i n e . I t i s \tan g e n t o f t h e a n g l e t h a t t h e l i n e m a k e s w i t p o s i t i v e x - a x i s I f a l i n e m a k e a n g l e α w i t h p o s i t i v e x - a x i s k = \tan α

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