In this activity, students use graphing technology to see how adjusting different parts of a linear equation affect its graph. This connects to the associated Algebra 1 lesson where students will look at similar effects to quadratic equations. When students vary the parameters in a linear function and record their observations, they have an opportunity to attend to precision through their word choices (MP6).

The goal of this discussion is to clarify how adjusting different parts of a linear equation affect its graph.

Direct students’ attention to the reference created using Collect and Display. Ask students to share their observations. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

Display a graphic organizer with categories corresponding to the moves in the activity, for example:

As students share their observations for each move, record the effect in the organizer, along with any example equations or graphs that they mention.

This activity is an opportunity to practice evaluating quadratic expressions for a negative value of the variable and choosing parameters of an equation that will result in its graph looking a certain way. Students’ repeated work with evaluating quadratic expressions involving negative values allows them to express regularity in repeated reasoning (MP8).

The goal of this discussion is to summarize the ways changing parts of an equation change a graph. Invite students to share various equations that each graph could represent. Use different but equally correct equations to help students generalize. For example, either or makes sense for Graph C, because it looks like , and is shifted up by some number between 10 and 20. So we know that the equation this graph represents is in the form , where is positive, even though we can’t tell its exact value from the given information. Here are some questions for discussion:

• “All of these equations are possible representations of Graph C. What do they have in common?” (They have a positive slope. Their slope is 1 because it is not steeper or less steep than the graph of . The -intercept is greater than 10 but less than 20.)
• “If you were shown the graph of any linear equation, what would you look at to approximate the equation?” (I would look at the -intercept to see if it is positive or negative and around what number it would be. I would also look at the slope to see if it is positive, negative, 0, or undefined and if the graph looks more or less steep than .)