Many physical quantities are linearly related. For example, consider Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. This is a linear relationship, expressed as F = MA. This linear equation can be used to solve for any of the three variables, given the other two are known or can be derived.
Linear equations can be used when grocery shopping to calculate the right amount of food to buy. One such equation could be (Quantity to purchase) = (Number of meals) * (Number of people) * (Quantity per meal) -- (Quantity already purchased). Using this equation, you could figure out how many apples you need to buy, if your three children each have an apple in their lunch five days a week, and you currently have four apples in the refrigerator: (Quantity to purchase) = (5 meals) * (3 kids) * (1 apple each) -- (4 apples in the fridge) = 11 apples.
Some simple population changes can be modeled with linear equations. Consider, for example, a college that accepts 2,000 new students every summer, and which loses 25% of its student body every year due to graduation or drop-outs. The student population might be modeled as (Population next year) = .75(Population this year) + 2,000. This linear equation could be used to make decisions about the college's needs for dorm rooms, teachers, or classroom space, based on the expected changes to the size of the student body.
In economics, linear equations can be used to calculate profits from costs and revenue. In a simple case, profit may be considered as revenue minus costs, or P = R -- C. Revenue could be calculated as the product of the quantity of items sold and their price, or R = (items) * (price). Costs can be calculated by considering the sum of the fixed costs and the cost per item, or C = (fixed) + (cost) * (items). Putting these two linear equations into the profit equation, the result is Profit = (items) * (price) -- ((fixed) + (cost) * (items)). This equation could be used to calculate expected profits, or to determine pricing requirements or cost cuts needed to reach a desired profit, for a given quantity of product sold.