# 1: Linear Equations and Lines

- Page ID
- 40091

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Learning Objectives

In this chapter, you will learn to:

- Solve linear equations
- Solve linear inequalities, expressing solutions on a number line and in interval notation
- Graph linear equations
- Find the equation of a line
- Apply linear models to data

- 1.1: Solving Linear Equations and Inequalities
- An equation is a statement indicating that two algebraic expressions are equal. A linear equation with one variable, x , is an equation that can be written in the standard form ax+b=0 where a and b are real numbers and a≠0 . A solution to a linear equation is any value that can replace the variable to produce a true statement.

- 1.2: Graphing Linear Equations
- Equations whose graphs are straight lines are called linear equations. A line is completely determined by two points. Therefore, to graph a linear equation we need to find the coordinates of two points. This can be accomplished by choosing an arbitrary value for x or y and then solving for the other variable.

- 1.4: Linear Applications
- Now that we have learned to determine equations of lines, we get to apply these ideas in a variety of real-life situations.

- 1.5: Fitting Linear Models to Data
- 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.