Direct and Inversely Proportion

Direct Proportion

Two variables are direct proportional if there is always a constant ratio between them.
(As one variable increases, the other also increases.)

$\frac{y}{x} = k$

$y = k \cdot x ↓ \begin{matrix} a & c \\ b & d \end{matrix} ↓ a : b = c : d a \cdot d = b \cdot c$

(The direction of the arrows follows the growth of the variables.
When committing proportionality, follow the arrows direction!)

Example:
2 books cost 6 euros. How much do 10 books cost?
(direct proportion: more books - more money) $↓ \begin{matrix} 2 b o o k s & 6 € \\ 10 b o o k s & x € \end{matrix} ↓ \Rightarrow 2 : 10 = 6 : x \Rightarrow x = 30$

Inversely Proportion

Two variables are inversely proportional if the product of those variables is a constant.
(As one variable increases, the other decreases.)

$y \cdot x = k$

$y = \frac{k}{x} ↓ \begin{matrix} a & c \\ b & d \end{matrix} ↑ a : b = d : c a \cdot c = b \cdot d$

(The direction of the arrows follows the growth of the variables.
When committing proportionality, follow the arrows direction!)

Example:
20 workers finish a job in 20 days. In how many days will 5 workers finish the same job?
(inversely proportion: more workers - less days) $↓ \begin{matrix} 2 w o r k e r s & 20 d a y s \\ 5 w o r k e r s & x d a y s \end{matrix} ↑ \Rightarrow 2 : 5 = x : 20 \Rightarrow x = 8$

Keywords:

Polynomials
Special Binomials
Progressions
Arithmetic progression
Geometric progression
Logarithm
Logarithm
Changing the base of a logarithm
Exponents
Powers
Roots
Roots
Proportionality
Direct and Inversely Proportion
Inequalities
Inequalities
Equations
Quadratic equation
Cubic Equations
Irrational and transcendental equations
Complex numbers
Complex Numbers
Adding and Subtracting Complex Numbers
Multiplying and Dividing Complex Numbers
Power of complex numbers
Roots of complex numbers
Kamatni račun
Interest calculation,
Matrices
Definition, adding & subtracting of matrices
Multiplying matrices