Students practice writing equations for lines parallel and perpendicular to a given line. Monitor for students who use slope-intercept form for the first question and for those who use point-slope form.

If students calculate an incorrect value for the slope of a line perpendicular to , ask them to check their work by multiplying the original slope and their proposed perpendicular slope. If the result is not -1, something is wrong.

If possible, invite one student who used point-slope form and another who used slope-intercept form to share their solutions. If no student used slope-intercept form, ask students if we have enough information to use the form . After both equations are displayed, challenge students to rearrange one of the equations to show they’re equivalent.

This activity gives students an opportunity to determine and request the information needed to graph a line and write the equation that represents it.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for the information they need in order to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and to ask increasingly more precise questions until they get the information they need (MP6).

There are several possible equivalent equations for each Problem Card. The equations students write will depend on the information they elicit from their partner. Monitor for different solutions to highlight during the Activity Synthesis.

Students apply the theorems they proved in the previous activities to problems. First, students write an equation of a perpendicular line by recognizing that the slopes must have a product of -1. Next, students explain why two lines that are both perpendicular to the same line must be parallel.