Graphing Linear Functions Using Intercepts

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Objective

SWBAT graph a linear function using the x and y-intercepts.

Big Idea

Finding the intercepts of a function can be a useful way to determine some coordinates that satisfy the equation of that function.

Launch

10 minutes

In my class, most students will be familiar with the context of intercepts_linear_launch from earlier in the year.  Today, students can work in pairs to make a mathematical model such as a graph to show all of the possible combinations.  Take the time to have students plot points on the board as was done in the first Groupon lesson (see understanding and extending equations unit) however, this may not be necessary.

Project the second slide of intercepts_linear_powerpoint and have students do a think-pair-share. Have each student individually write down the meaning and then share that response with their partner (MP1).  Between the two of them, have them come up with the best meaning possible for the two coordinates (MP3).  As students are discussing this, listen in for students that are grasping the idea that when one variable is zero the other must be 25.  Also, listen for any students that are using the term intercept. 

During the whole class share-out, have students who mentioned the ideas above share out. If the word "intercept" does not naturally come up, guide students to come up with that word. When possible, use geometric descriptions to help students grasp the meaning of intercept.  For example, the height of the graph on the x-intercept is zero.  This means that the y-value must be zero.  The distance left or right on the y-intercept is zero.  This means that the x-value must be zero.  

Next, ask students how many points are needed to make a unique straight line?  Have them turn and talk about the answer to this question.  Once students all understand why the answer is 2, explain to them that if they can plot both the x-intercept and the y-intercept in the coordinate plane that will be enough to graph a unique line.  

Ask students, why is it sometimes easier to graph the intercepts than other points?  Answer: Plugging in 0 is usually easier than plugging in another number (MP2).

Practice

20 minutes

During this section of the lesson students practice graphing linear equations using intercepts. You can begin by choosing one of the questions on intercepts_linear_graphing and guide students through how to graph the equation.  Try not to simply show students, ask them questions that will help others understand the concept behind finding the x- and y-intercepts and graphing these points.  

After the demonstration, use your judgment to assign a selection of problems from the worksheet. Depending on time and the ability of the class, you can assign all of the questions or just certain ones.  Expect that students who have difficulty with algebraic manipulation may struggle to work quickly and accurately.  This would be a good time to differentiate the lesson by working more directly with one or more groups of students.  

For an independent practice session like this, I like to have an answer key posted somewhere in the room so that students can check it during their work to ensure they are on the right track. This also helps to promote independence and self-advocacy among students in the class.

Closure

10 minutes

This ticket out the door will require students to process the idea of intercepts on a deeper cognitive level.  Students will be designing their own question that can be represented by the given mathematical model (MP4).  (Tell students that there are no $10 Groupons...in other words, be creative and do not just reuse the example from class with different numbers!)  If there is time at the end of class have a few students share their problems.  Challenge other members of the class to determine the meaning of the x and y-intercept based on the context of the problem.