Linear equations use one or more variables where one variable is dependent on the other. Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit. Many people use linear equations every day, even if they do the calculations in their head without drawing a line graph.

## Variable Costs

Imagine that you are taking a taxi while on vacation. You know that the taxi service charges $9 to pick your family up from your hotel and another $0.15 per mile for the trip. Without knowing how many miles it will be to each destination, you can set up a linear equation that can be used to find the cost of any taxi trip you take on your trip. By using "x" to represent the number of miles to your destination and "y" to represent the cost of that taxi ride, the linear equation would be: y = 0.15x + 9.

## Rates

Linear equations can be a useful tool for comparing rates of pay. For example, if one company offers to pay you $450 per week and the other offers $10 per hour, and both ask you to work 40 hours per week, which company is offering the better rate of pay? A linear equation can help you figure it out! The first company's offer is expressed as 450 = 40x. The second company's offer is expressed as y = 10(40). After comparing the two offers, the equations tell you that the first company is offering the better rate of pay at $11.25 per hour.

## Sciencing Video Vault

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## Budgeting

A party planner has a limited budget for an upcoming event. She'll need to figure out how much it will cost her client to rent a space and pay per person for meals. If the cost of the rental space is $780 and the price per person for food is $9.75, a linear equation can be constructed to show the total cost, expressed as y, for any number of people in attendance, or x. The linear equation would be written as y = 9.75x + 780. With this equation, the party planner can substitute any number of party guests and give her client the actual cost of the event with the food and rental costs included.

## Making Predictions

One of the most helpful ways to apply linear equations in everyday life is to make predictions about what will happen in the future. If a bake sale committee spends $200 in initial start up costs and then earns $150 per month in sales, the linear equation y = 150x - 200 can be used to predict cumulative profits from month to month. For instance, after six months, the committee can expect to have netted $700 because (150 x 6) - 200 = $700. While real world factors certainly impact how accurate predictions are, they can be a good indication of what to expect in the future. Linear equations are a tool that make this possible.