Equation of a Line

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

In this lesson, we will learn

  • slope-intercept form of a line
  • point-slope form of a line
  • standard form of a line
  • applications of linear equations

 

 

Slope-Intercept Form of a Line

Slope-intercept form of a line is a general formula for the equation of a line. Using the slope-intercept form of a line helps in finding the slope of a line from an equation and the intercept directly from the equation. This is great because it shows how to graph a line using y = mx + b and can be quite useful for applications of linear equations.



This video explains how to graph a linear equation given in slope intercept form.

 

 

This video provides an example of how to graph a line in slope intercept form with a positive fractional slope and a whole number y-intercept.



This video provides an example of how to graph a line in slope intercept form with a negative fractional slope and a negative y-intercept.



This video provides an example of how to graph a line in slope intercept form with a negative integer slope and a positive integer y-intercept.



 

 

Point-Slope Form of a Line

Point-slope form of a line is one method to write the equation of a line. Start with the slope equation, which is basically the difference between two points, and then rearrange the terms to obtain the point-slope form of a line. The point-slope form of a line provides a formula that is useful in finding the slope of a line from an equation and a point the line passes through.



This video provides two examples of how to graph a linear equation in point-slope form.

 

 

Standard Form of a Line

We will commonly see lines expressed standard form, especially when we look at and write systems of linear equations. The standard form of a line 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.

This video explains how to write a linear equation in standard form, how to determine the equation of a line in standard form, and how to graph a line in standard form. 



This video provides an example of how to graph a linear equation in standard form with fraction coefficients by solving for y and writing the equation in slope intercept form.



 

 

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.

 

 

 

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