This warm-up will give students more work with algebraically manipulating an equation in two variables. Have students work on the two problems by themselves first and then turn and talk with their partner to compare their answers. When students are comparing answers encourage them to discuss how they determined the slope and y-intercept of each equation (MP3). As you are monitoring student discussions, listen for those that are making good justifications for their work. You can ask a pair of students to model their discussion for the class as a model of how a solid discussion will sound.
The purpose of this practice is to help students develop fluency around the three different techniques for graphing a linear equation (finding intercepts, plotting points that make the equation true, and putting the equation in slope-intercept form).
Depending on your class, you may want to work through the first question together as guided practice. In either case, as students are working, ask them to pay attention to which technique seems to work best for each equation (MP7). Students will notice that one technique may work better than another based on the structure of the equation. The equations were also chosen so that one technique will appear to be more advantageous on certain questions.
In each question, the students will be graphing the same equation three times. The advantage to this type of practice is that students have a built-in check for each question. Since students will be graphing the same linear equation, if one graph looks different from the others students know that they need to check their work for correctness (MP6).
In this ticket out the door students will be evaluating an equation to determine which graphing technique will be most advantageous (MP1 & MP2). Students will need to justify their choice through a written explanation (MP3). In this ticket out, it is expected that many students will choose either intercepts or point-plotting. However, an argument could be made for any of the three techniques. The idea is that students have an opportunity to choose a technique and use mathematical language to justify their choice.