Formulas and ProblemSolving
Linear equations can be used to solve many everyday and technically specific problems.
Learning Objective

Use a given linear formula to solve for a missing variable
Key Points
 A linear equation can be used to solve any problem that includes constants and variable(s) of first order.
 A linear equation can be solved for any one variable provided that the values of all other variables are known.
 Linear equations can be used to calculate tip, cost of goods, velocity, simple interest, and many more variables.
Terms

line of credit
A financial agreement under which a bank or other lender agrees to provide a client with loans of money up to an approved limit during a predefined period. The client may borrow the entire credit amount all at once or in portions during the specified period.

principal
The money originally invested or loaned, on which basic interest and returns are calculated.
Full Text
Linear equations can be used to solve many practical and technical problems. Such an equation may include many variables so long as all are of the first order, and the value of any one variable can be calculated if the values of all the other variables are known.
For example, one can use a linear equation to determine the amount of interest accrued on a home equity line of credit after a given amount of time. Consider the hypothetical situation in which you need money to make home improvements and can open a $20,000 credit line at an interest rate of 2.5% per year. You plan to pay off the debt in its entirety within 15 months. To find out how much it will cost you can use following formula:
Where I is interest, p is the principal amount loaned ($20,000), r is the interest rate (2%, or 0.02) per year, and T is the number of years elapsed (15 months will be 1.25 years).
Plugging the known values into the above formula, we can determine that you will pay $500 in interest.
There are many other common formulas that can be used for everyday computations. Some have more variables than others, but none has a variable of order higher than one. Let's take a few examples of other linear equations, namely velocity, gratuity (tip), and cost of purchased goods:
The formula relating velocity (V), distance (d), and time (T).
Interactive Graph: Gratuity as a Function of Bill Price
Graph of gratuity as a function of the price of the bill, y=0.18x, where gratuity of 18%. The dependent variable (y) represents gratuity (tip) as a function of cost of the bill (x) before gratuity. How would the equation change if you wanted to tip 20%?
The formula relating gratuity (G), cost (c), and desired percent gratuity (r, expressed as a decimal).
Where A, B and C represent the quantities of goods that cost x, y and z, respectively. This could be expanded or contracted relative to the number of different items purchased. T represents the total cost of goods purchased.
Key Term Reference
 Interest
 Appears in these related concepts: Interest Compounded Continuously, Accounting for Interest Earned and Principal at Maturity, and Tax Considerations
 constant
 Appears in these related concepts: Graphing Quadratic Equations in Vertex Form, Inverse Variation, and Direct Variation
 distance
 Appears in these related concepts: Inequalities with Absolute Value, The Distance Formula and Midpoints of Segments, and Linear Mathematical Models
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 linear
 Appears in these related concepts: Exponential Growth and Decay, Graphs of Linear Inequalities, and Factoring General Quadratics
 linear equation
 Appears in these related concepts: Rates of Change, Linear Inequalities, and Solving Systems of Equations Using Matrix Inverses
 percent
 Appears in these related concepts: Circles as Conic Sections, Percents, and ProblemSolving
 variable
 Appears in these related concepts: What is a Linear Function?, Math Review, and Introduction to Variables
 velocity
 Appears in these related concepts: Velocity of Blood Flow, RootMeanSquare Speed, and Rolling Without Slipping
Sources
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