Have students work to graph these three equations in any way they would like (slope-intercept method, using intercepts, making a table, etc.) Students will notice rather quickly that all three are representative of the same equation. The question is why? Let students work in pairs to determine why all of these equations are actually the same (MP3). Some students will use algebraic manipulation to show why they are the same. Others may reason about it by using values for x and y (MP2). In either case, we are planting the seeds to have students be able to write equations in a variety of ways and noticing that their structure can give clues as to the way an equation will appear (for example, slope-intercept form)
For this activity, the outcomes may be very open ended. Try to call on students to share their results that will offer explanations that are insightful but not confusing. There will be more time spent in future lessons on writing functions in certain forms.
modeling_linear_functions gives students a chance to practice using mathematical modeling applied to real-world contexts (MP4). In each of these examples, students will be identifying the rate of change and y-intercept in context and using their mathematical model to answer a predictive question. Students will also be practicing their precision (MP6) by scaling and labeling their axes appropriately in each case.
If time permits, have students use the document camera to show their solutions to a particular quesiton and allow their classmates to ask questions about their work.
Now that students have seen several questions dealing with applying a linear function to a real world context they will be making one of their own. Students will write out the scenario and then write a predictive question that goes along with it. Once a pair of students is each done, they should swap questions. They will first write a function that will model the situation and then answer the predictive question. While engaging in the question, students should be encouraged to provide feedback to their partner that will make their question even better, more interesting, more understandable, etc. (MP3). This work can be collected and used later on as homework or formative assessment items (students love when their work is "published" and is completed by all the students in their class).