 # Linear Equations

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A series of free, online Basic Algebra Lessons or Algebra I lessons.
Videos, worksheets, and activities to help Algebra students.

In this lesson, we will learn

• How to Write Equations in Slope-Intercept Form
• How to Graph Lines using a Table of Values
• The Applications of Linear Equations
• The Standard Form of a Linear Equation

### Writing Equations in Slope-Intercept Form

Intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y = mx+b. Other forms of linear equations are the standard form and the point-slope form.

Finding Slope and Writing Linear Equations in Slope-Intercept Form
This video looks at writing equations in slope-intercept form, given either two ordered pairs, or an ordered pair and a slope. It includes four examples. Linear Equations in Slope Intercept Form

### Graphing Lines using a Table of Values

When first introduced to graphing lines, we often use a table of values to plot points and connect them. There are several other methods of graphing lines, including using a point and the slope. Sometimes graphing lines using an equation involves the same methods as using a table of values. Since we graph lines in the coordinate plane, it is necessary to understand how to connect graphs, tables and equations.

Graph a Linear Equation Using a Table of Values
This video provides an example of graphing a line solved for y using a table of values

Graph a Linear Equation Containing Fractions Using a Table of Values
This video provides an example of graphing a line solved for y containing fractions using a table of values.

### Applications of Linear Equations

We often see math applied to the real world through word problems, and the applications of linear equations are seen throughout all our math courses after Algebra. To understand applications of linear equations we need to have an understanding of slope, how to interpret a graph, and how to write an equation. In upper-level Algebra, we apply systems of linear equations to these problems as well.

Given a Linear Model, Interpret the Meaning of the Slope and Make Predictions
In this video, a linear equation is given in slope intercept form to model the descent of the plane. The meaning of the slope is discussed and then the equation is used to answer various questions. Linear Equation Application (Cost of a Rental Car)
This video provides an example of how to determine how far you can drive a rental car with a specific amount of money to cover the fixed cost and mileage cost.

### Standard Form of a Linear Equation

We will commonly see lines expressed in the standard form of a linear equation, especially when we look at and write systems of linear equations. The standard form of a linear equation puts the x and y terms on the left hand side of the equation, and makes the coefficient of the x-term positive. While standard form is commonly, we sometimes rewrite a line in slope-intercept form in order to graph it.

Given Linear Equation in Standard Form, Write in Slope-Intercept Form to Graph
This video provides an example of how write an linear equation in standard form in slope intercept form to graph. This video provides an example of how write an linear equation in standard form in slope intercept form to graph.

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