In this lesson, students consider graphically and algebraically what it means to be a solution to an equation with two variables. Students begin by choosing a value for one variable in an equation and finding the value for the other variable that makes the equation true.

Next, they analyze statements about potential solutions to the equations defining three graphs. Students observe that when a point lies on two lines, such as at their point of intersection, then the coordinates of that point are solutions to both equations represented by the lines. This will be useful for thinking about what it means to be a solution to a system of linear equations in a following unit.

Then students consider equations given in different forms, ask their partner for either the - or -coordinate of a solution to the equation, and then find the missing value for the coordinate. Students are encouraged to use the structure of an equation and decide whether it would be more efficient to solve if given or given (MP7).