Math

Applications of Linear Functions

A mathematical model is a formula or an algebraic equation that can be formed using actual data. Linear equations are useful in modeling data that fall on a line. Consider the following example:

A rice dealer discovers a linear relationship between the number of sacks of rice he/she can sell and the price per sack of rice. A hundred sacks of rice can be sold at ₱1500 each, and 60 sacks can be sold at ₱1700 each. Let x be the number of sacks of rice sold and y be the price per sack of rice. Find the line determined by the two ordered pairs $(100, 1500)$ and $(60, 1700) .$

Let $(x_{1}, y_{1}) = (100, 1500)$ and $(x_{2}, y_{2}) = (60, 1700) .$

$y - y_{1}$	=	$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})$	Two-point form
$y - 1500$	=	$\frac{1700 - 1500}{60 - 100} (x - 100)$	Substitute the given values.
$y - 1500$	=	$- 5 (x - 100)$	Simplify.
$y - 1500$	=	$- 5 x + 500$	Apply the distributive property
$y + 5 x$	=	2000	Add 5x and 1500 to both sides.
$5 x + y$	=	2000	Rearrange the terms.

The equation $5 x + y = 2000$ is of the form $A x + B y = C .$ The linear equation $5 x + y = 2000$ represents the demand line for rice.