# Properties of the Cup and the Equation

In Module 3.2, we explored "Intercepts of Lines." In that module, we discussed that the y-intercept is the value of y for which x is equal to zero. Graphically, the y-intercept is that point where the graph of the line crosses, or intercepts, the y-axis. What does this have to do with our cups? **The y-intercept tells us the initial height of the cups**. A larger y-intercept means you've started with a taller cup.

There's another important relationship in this equation that can instantly tell you the rate at which the cups are growing: the slope. In fact, the concept of slope provides us with an important bridge between algebra and geometry. While students most commonly study equations of the form *y = mx + b* in algebra, there is a link to geometry in the principle that **two lines having the same slope are parallel**. Stated another way, if two stacks of cups are growing at the same rate (height per cup), then the graphs representing their heights are parallel lines.

Can they make the connection? View "The Equation and the Cup" in which Ms. England discusses with a group of students how the equation is related to various attributes of the cup.

**Classroom Clip Reflection:**

- What concepts do the students understand? Not understand?
- What other questions might you ask?
- What assessment might you give to check their understanding before students leave for the day?
- What are the implications for the students you work with?