Math 10C Module 6: Lesson 2

Module 6: Linear Equations

Lesson 2 Summary

In this lesson you investigated the following questions:

  • How are the properties of a linear function used to determine its equation?

  • In what ways does drawing a graph help you to solve math problems?

In this lesson you learned how to use given information to write the equation of a line. You used both the slope-intercept form and the slope-point form of a linear function to write linear equations. You learned that, in order to write the equation of a line, you need to know certain properties of the line. These properties are its slope of the line and a point through which the line passes. Sometimes you are not given a slope but only two points. In these cases, you can use the slope formula to determine the slope of the line. You watched videos and worked through interactive lessons that demonstrated how to determine the equation of a line.

In this lesson you compared two methods of identifying the properties of a linear function—graphically and algebraically. You may have discovered that it is easier in some instances to determine the properties of a line by sketching a graph. A graph can be a rich source of information about a math problem. A graph readily gives you a slope and the y-intercept. These values can then be used to determine the equation of the line in the form y = mx + b. The steepness of the line gives an indication of the rate of change of one variable with respect to another. The scale of each axis gives you an idea of the size of the quantities in the context of the problem.

While a graph can be helpful to you when solving problems, you may have also discovered that it is sometimes easier to determine a line’s properties algebraically. For example, when the y-intercept of a line is not an integer, it is much easier to determine its exact value algebraically as opposed to graphically.

In the next lesson you will examine the relationship between parallel lines. You will also examine the relationship between perpendicular lines. You will analyze their slopes and write equations of lines which are parallel or perpendicular to given ones.

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