### Linear Functions are Important. They are everywhere!

One reason that linear functions are so important is that in the simplest contexts where two variable measurements are made, the relationship between those variables are best described by a linear function.

Where do you find Linear Functions? The contexts for finding linear functions are all around us.

At home:

When we drive our cars (or bicycles), walk, or run at a constant speed on a road , the distance we travel is a linear function of time. If we let $s$ denote the distance along the road we have traveled, $t$ denote the time that has elapsed, and $r$ denote our rate of travel, then $s = r \times t$, "distance is rate times time."
The amount of gas consumed by a car is usually estimated as a linear function of the distance traveled.
If we let $g$ denote the amount of gas consumed on a trip, $s$ denote the distance along the road we have traveled, $r_g$ denote the rate at which gas is consumed by our car, then $g = r_g \times s$, "gas is rate of consumption times distance."

At the store:
When we purchase a commodity (vegetables, rice, oil, gasoline) at the market by weight or volume, the cost is a linear function of the amount being purchased.
If we let $C$ denote the cost of the commodity being purchased, $x$ denote the amount of the commodity we are buying, and $p$ denote the unit price of the commodity, then $C = p \times x.$, "cost is price times  amount purchased."
When we sell a commodity (vegetables, rice, oil, gasoline) at the market by weight or volume, the revenue is a linear function of the amount being sold.
If we let $R$ denote the revenue received for the commodity being sold, $x$ denote the amount of the commodity sold, and $p$ denote the unit price of the commodity, then $R = p \times x$, "revenue is price times  amount sold."

In Science:
When we convert measurements from the English to the metric system , the metric measurement is a linear function of the the English measurement. For example, if we let $F$ denote the temperature measured in the Fahrenheit scale and $C$ denote the same temperature measured in the Centigrade scale, then $F = \frac 9 5 C + 32$, a linear function.
When a object is moving freely in a fall above the surface of the earth, its velocity is a linear function of time.
If we let $v$ denote the velocity of the moving object, $t$ denote the time the object has been in free fall and $g$ denote the acceleration of the object due to the gravitational force of the earth, then $v = g \times t$, "velocity is acceleration times  time."