Direct variation describes a relationship between two variables in which one variable is a constant multiple of the other. In simpler terms, as one variable increases, the other variable increases proportionally, and as one decreases, the other decreases proportionally.

Equation: y = kx, where:

• y is the dependent variable
• x is the independent variable
• k is the constant of variation (also called the constant of proportionality)

Example: The distance traveled by a car moving at a constant speed varies directly with time. If a car travels 100 miles in 2 hours, the constant of variation (speed) is 50 mph. So, the equation is d = 50t, where d is the distance and t is the time.

Indirect variation (also known as inverse variation) describes a relationship between two variables in which one variable increases as the other decreases, and vice versa. The product of the two variables is constant.

Equation: y = k/x, or xy = k, where:

• y is the dependent variable
• x is the independent variable
• k is the constant of variation

Example: The time it takes to complete a job varies inversely with the number of workers. If it takes 4 workers 6 hours to complete a job, the constant of variation is 24. So, the equation is t = 24/n, where t is the time and n is the number of workers.