Lesson 3: Slope Intercept Form
Module 5: Linear Functions
Lesson 3 Summary
In this lesson you investigated these following questions:
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How does the equation of a linear function relate to its graph?
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How are the properties of linear functions applied to studying and solving problems?
In this lesson you learned that a line can be represented by the equation y = mx + b. This is called slope-intercept form. You discovered that the slope of the graph is given by the value of m in the equation and the y-intercept is given by the value of b in the equation.
You can graph a linear function easily when it is presented as an equation in slope-intercept form. You do this first by identifying and plotting the y-intercept, b. Then you can apply the slope, m, to the y-intercept in order to find a second point. By connecting the two points, you will have a line that corresponds with the given slope and y-intercept.
In this lesson you also practiced solving contextual problems involving slope, y-intercept, domain, and range. When placed in the context of a real-world problem, the properties of linear functions have meaning. The y-intercept of a distance-time graph may refer to the distance that an athlete has to run in a triathlon while the x-intercept may refer to the time that it takes to run that distance.
In previous lessons you learned that the domain and the range of diagonal lines are elements of the real numbers. The domain and the range of a linear relation in a real-world setting, however, may have to be restricted to those points which are meaningful. Negative values and very large numbers are often unrealistic or not meaningful in the context of everyday situations. When using linear functions to model problems, it is not enough to complete the math correctly but it is also important to assess whether the results make sense in the context that the results are being used in.
In subsequent lessons you will learn how to represent linear functions with equations of other forms. You will learn the type of information that each equation gives and you will study how to use these equations to graph linear functions.