Lesson 4: General Form and Slope-Point Form
Module 5: Linear Functions
Lesson 4 Summary
In this lesson you investigated the following questions:
- How are the general, slope-intercept, and slope-point forms different from each other?
- Why are there multiple ways of expressing linear functions?
There are multiple ways of representing the equation of a linear function. In Lesson 3 you studied the slope-intercept form. In this lesson you examined the slope-point form and the general form.
Here is a nice graphic to summary how to change between the forms.
In the Going Beyond section of this lesson, you may have discovered even more ways that a linear equation can be expressed. Besides learning about the different forms, you also learned how to convert between forms. Specifically, you learned how to convert a linear equation from slope-intercept and slope-point forms into general form and from general form to slope-intercept form. Each method of representing a linear equation has its benefits. Both the slope-intercept form and the slope-point forms are useful for graphing since you can easily extract a point and the slope from each form.
General form is different from the slope-intercept and slope-point forms in two key ways. First, the coefficients are integers or whole numbers. This means that equations in general form will not contain fractions or decimals. Second, the terms of an equation expressed in general form will all be on the same side of the equation. While the slope and y-intercept are not directly given in general form, you can still determine those properties of the linear function by rearranging the equation into one of the other forms.
It is helpful to have multiple ways of representing an equation since this allows you the flexibility of interpreting and presenting a linear relation based on the information that is available. In this lesson you have learned to identify equivalent linear relations from a set of linear relations. One approach is to rearrange equations into slope-intercept form. You can then compare the slopes and intercepts. In the next lesson you will apply the information about the three equations you learned, and you will create graphs for all three equation types.