6: Linear Functions
Recall that a function is a relation that assigns to every element in the domain exactly one element in the range. Linear functions are a specific type of function that can be used to model many real-world applications, such as plant growth over time. In this chapter, we will explore linear functions, their graphs, and how to relate them to data.
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- 6.1: The Rectangular Coordinate Systems and Graphs
- Descartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the \(x\)-axis and the vertical axis the \(y\)-axis. This system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the \(x\)-axis and the \(y\)-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant.
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- 6.2: Linear Functions
- The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a linear function is also known as the slope. An equation in the slope-intercept form of a line includes the slope and the initial value of the function. The initial value, or y-intercept, is the output value when the input of a linear function is zero.
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- 6.5: Exercises
- Scatter plots show the relationship between two sets of data. Scatter plots may represent linear or non-linear models. The line of best fit may be estimated or calculated, using a calculator or statistical software. Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data. The correlation coefficient, r , indicates the degree of linear relationship between data.