In this Warm-up, students match linear equations to their graphs, then find points on each line and interpret them in the situation. This work prepares students for later in the lesson when they interpret values in similar situations. Students reason abstractly and quantitatively (MP2) when they make connections between the representations of a situation.

The purpose of the discussion is to help students connect the situation to the equations and graphs. Select students to share their solutions. Here are some questions for discussion:

• “Which plant has a greater value for the slope? What does the value mean in terms of plant growth?” (Plant A has a greater slope since . This means that every 2 weeks, Plant A grows 1 inch.)
• “What do the vertical intercepts mean for these plants?” (They represent the height of the plants when they were found.)
• “What do the horizontal intercepts mean for these plants?” (They represent the time when the plants just broke through the ground.)
• “Do negative - and -values make sense in this situation?” (Yes, to a point. The plants were growing before they were found, so some negative -values can make sense. The seeds for these plants were also underground at some point, so the plant could be considered to be below ground level, which would give meaning to negative -values.)

In this activity, students interpret a quadratic equation in a situation. In the associated Algebra 1 lesson, students solve quadratic equations in situations. This activity supports students by helping them connect the equation to the situation. Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).

In this activity, students solve a system of linear equations in a given context. In the associated Algebra 1 lesson, students solve a system of equations involving a quadratic equation. This activity supports students by reminding them of methods used to solve systems of equations. Students look for and make use of structure (MP7) by pulling on prior experience with systems of equations and using the structure of the graphs and equations to find solutions.