This Warm-up activates some familiar skills for writing and solving equations, which will be useful for specific tasks throughout the lesson.

It may have been a while since students thought about writing an equation for a line passing through two points. The two questions here are intentionally quite straightforward. Monitor for students taking different approaches, such as:

• Plotting the points and determining the slope and -intercept of a line passing through the points.
• Computing the slope by finding the quotient of the difference between the -coordinates and the difference between the -coordinates.
• Considering which operation on each -coordinate would produce its corresponding -coordinate.

Students have not yet solved a quadratic equation like the one in the second question, but they have learned and extensively practiced the skills needed to solve it. The two main anticipated approaches are:

• Reasoning algebraically, by performing the same operation to each side of the equation, applying the distributive property to expand factored expressions, combining like terms, rewriting an expression in factored form, and applying the zero product property
• Graphing and and observing the -coordinate of each point of intersection

Invite students taking different approaches to share their work. Ensure that students see more than one way to think about the equation representing a line for the first question and recognize that the second equation can be solved algebraically.

Monitor for students taking different approaches, such as:

• Graphing the function and finding and interpreting points on the graph.
• Evaluating the function at relevant values.
• Writing and solving equations whose solutions answer the questions. Some equations can be solved by rewriting it as a factored expression equal to 0, while some must be solved by completing the square or using the quadratic formula.
• Rewriting the given expression in a different form—for example, rewriting it in vertex form to find the maximum value of the function.

If any students take a graphing approach and finish quickly, challenge them to verify their solution to each problem by using a second method that does not rely on graphing.

The purpose of this activity is for students to use what they know to solve an unfamiliar problem. Since it is unfamiliar, students need to make sense of the problem and demonstrate perseverance (MP1). This is a preview of using algebra and graphing to solve a system consisting of a linear equation and a quadratic equation, which students will study more in depth in a future course.