In this activity, students work to solve linear equations and recognize the solution in graphs. This skill will help students when they examine quadratic equations and their solutions in the associated Algebra 1 lesson. Students reason abstractly and quantitatively (MP2) when they interpret the meaning of solutions in the context of situations.

The purpose of the discussion is to notice the connection between solutions of equations and the graph of both sides of the equation. Select students to share their solutions. Here are some questions for discussion:

• “Why are both solutions to these questions related to the horizontal intercept?” (Since both questions asked about when the value is 0, it makes sense to look at the points where which is along the horizontal axis.)
• “How could you find the worth of the electronic device after 4.5 years?” (Substitute 4.5 for in the equation, and solve for the value.)
• “How could you find the number of minutes it takes to reach an elevation of 100 feet above sea level?” (Substitute 100 in the equation for , and solve for .)

In this activity, students practice solving equations and seeing the solution in graphical form. The questions in this activity are not restricted to problems where the equation is equal to zero. Students must recognize that solutions to these equations may involve either rewriting the equation to equal zero before graphing or solving a system of equations with each side of the equation representing a function to be graphed. As students interpret the meaning of their solutions in the context of each situation, they reason abstractly and quantitatively (MP2).

The purpose of the discussion is for students to see how solutions to equations can be seen in a graph. Select students to share their solutions. Here are some questions for discussion:

• “How do the equations for the first 2 questions differ from the others in this lesson?” (The equations are equal to a non-zero constant.)
• “What does the horizontal intercept mean in the bookstore situation? Is it realistic?” (It means the number of books ordered that would cost $0. The solution is a negative number of books since there is a delivery fee, so this does not make sense in reality.)