Lesson 5: Graphing Linear Functions

Math 10C Module 5: Lesson 5

Module 5: Linear Functions

Lesson 5 Summary

In this lesson you investigated the following questions:

->In what ways can you verify that you have properly graphed a linear function?

->How is graphing a linear relation similar to solving the corresponding equation?

In this lesson you explored strategies for graphing linear functions. To graph a line, you need to know either of the following:

->two points on the line

->one point on the line and its slope

The strategies you used depended on the form of the linear equation. For linear functions expressed in slope-intercept form or slope-point form, you are directly given the slope of the line as well as a point on the line. In the case of the equation y = mx + b, m is the slope and (0, b) is the y-intercept. In the case of the equation y − y₁ = m(x − x₁), m is the slope and (x1, y1) is a point on the line.

For linear functions expressed in general form Ax + By + C = 0, you learned two main approaches for graphing.

The first approach is to convert the general form into slope-intercept form. When this is done, the slope is and the y-intercept is .

The second approach is to find two points on the line. Sometimes, the intercepts of the graph are easy to find and result in coordinates that are integers. When this is not the case, you can employ a system of trial and error to find points other than the intercepts which have integral coordinates.

Graphing a linear relation is similar to solving the corresponding equation in a couple of ways. In solving an equation, you are balancing both sides of the equation with the aim of isolating a particular variable. In graphing a linear relation, you may rearrange general form into slope-intercept form with the aim of isolating y. A second way that graphing a linear equation resembles the solving of an equation is in the way that points on the line are determined. In order to find a point on the line, whether it is an intercept or not, you need to substitute a value for x or for y. By doing so, you have made it possible to solve the equation for the other variable.

Verifying an equation can be done by selecting two points on the graph and substituting their coordinates into the equation of the line. If the result is a true statement for the coordinates of each point, then the line is considered correct. Since you have learned multiple strategies for graphing linear functions, another way to verify a graph is to employ a different approach to graph the line and then compare the result with the first graph.

You have now completed Module 5. In the next module you will learn about parallel and perpendicular lines and how to write the equations of linear equations. All of these outcomes were taught in the context of recreational pursuits and hobbies!