# Algebra and real life linear relationships

Learning Objectives Apply linear mathematical models to real world problems Key Takeaways Key Points A mathematical model describes a system using mathematical concepts and language.

Example Points: The points are graphed in a scatterplot fashion.

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. How fast was his average speed over the course of the run?

Rates Linear equations can be a useful tool for comparing rates of pay. The equation and graph can be used to make predictions.

Outlier Approximated Line: Here is the approximated line given the new outlier point at -1, 6. Linear equations are a tool that make this possible.

## Algebra and real life linear relationships

Notice 4 points are above the line, and 4 points are below the line. At pm he starts to run and leaves his home. Plugging it into the first equation gives us [latex]50 2. Updated March 13, By Jessica Smith Linear equations use one or more variables where one variable is dependent on the other. Key Terms mathematical model: An abstract mathematical representation of a process, device, or concept; it uses a number of variables to represent inputs, outputs, internal states, and sets of equations and inequalities to describe their interaction. The two trains meet at the intersections point [latex] 2. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a greater degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data. Anything that involves a constant rate of change can be nicely represented with a line with the slope. Real world applications can also be modeled with multiple lines such as if two trains travel toward each other. Linear equations are a tool that make this possible. Our second point is [latex]1. Indeed, so long as you have just two points, if you know the function is linear, you can graph it and begin asking questions! Rates Linear equations can be a useful tool for comparing rates of pay. One difficulty with mathematical models lies in translating the real world application into an accurate mathematical representation. Learning Objectives Apply linear mathematical models to real world problems Key Takeaways Key Points A mathematical model describes a system using mathematical concepts and language.

The simplest and perhaps most common linear regression model is the ordinary least squares approximation.

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