A. Slope-Intercept Form of a Linear Equation

Explore the Lesson

In Unit 6, you learned about linear relations. An equation that is used to represent a linear relation is called a linear equation. This unit focuses on representing linear relations using equations and graphs, and how these two representations are related.

Linear Equation A linear equation contains terms of degree 0 and/or 1. Linear equations are often used to represent linear relations.

 

A. Slope-Intercept Form of a Linear Equation

A relation can be graphed by using its equation to determine specific points on the graph and then plotting those points. This method is straightforward, but it can be fairly time consuming. Fortunately, when equations of linear relations are written in a specific format, they are more easily interpreted and they can be used to graph the linear relation more efficiently. In the Warm Up, you may have noticed that rearranging the equation of a relation did not change the relation itself. As such, the equation of a relation can be manipulated into a desirable format without changing the relation.

One such specific format is called the "slope-intercept form". When the equation of a relation is written in slope-intercept form, some characteristics of the relation and its graph can be interpreted directly from the equation. With practice, you will be able to visualize the graph of a relation by just looking at its equation.

 

Investigation

If you are unable to access the applet, skip ahead to the Alternate Investigation on the following page.

Slope Intercept

30 January 2014, Created with GeoGebra

1. The applet shows the equation of a relation in slope-intercept form and its graph. Try adjusting the m and b values. Turn on "show points" to see how individual points on the graph are affected by the m and b values.
   
   

   1. How does changing the m-value affect the graph?
      
      

   2. How does changing the b-value affect the graph?
      
      
      

2. Turn on "show points" if you haven't done so already.
   
   

   1. Use two points to determine the slope of the line currently showing.
      
      

   2. How is the slope related to the equation of the line?
      
      

   3. Adjust the m and b values and repeat part a. Is the relationship you determined in part b. still true?
      
      

   4. The b-value is related to where the graph crosses an axis. Describe this relationship.
      
      

3. Explain why the equation is referred to as the slope-intercept form of the equation of a line.