A direct variation model can be written in the form y=kx where k is said to be the constant of proportionality. Y is said to vary directly with x, or y is proportional to x. If x increases so does y, and if x decreases y does so also.

(1) The formula d=rt where d is a distance, r a rate, and t the time represents a direct variation model. As written, for a constant speed (r as the rate), d the distance varies directly with t time. (e.g. if you drive at a constant speed, say 60mph, the distance increases the longer you drive by a constant 60 miles every hour driven.)

Rewritten as d=tr we see that distance can vary directly with the speed for a fixed (constant) time. Thus is we drive for exactly one hour, we will cover more distance if the speed is increased.

(2) If you are paid an hourly wage, your gross income varies directly with the number of hours you work (excluding overtime, holiday pay, etc...) If I make $10 per hour, then my gross pay is G=10t where t is the number of hours I worked.

(3) The formula f=ma where f is the force, m the mass of an object, and a is the acceleration shows that the force varies directly with the acceleration. (Throw something harder and the impact is greater.)

(4) In chemistry we have PV=nRT, the ideal gas law. P is the pressure exerted, V is the volume, n is the amount of gas, R is a constant, and T is the temperature. From the formula we see that the pressure varies directly with the amount of gas, and is also proportional to the temperature. (We say that the pressure varies jointly with the amount of gas and the temperature.) Also, the volume varies jointly with the amount of gas and the temperature.

(5) In business we have R=C*CC where R is the retail price, C is the cost, and CC is the cost complement.

(6) `F=(Gm_1m_2)/r^2 ` is Newton's gravitational Law. The force of attraction varies jointly with the masses of the objects. (G is the gravitational constant.)

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