In the previous lesson students learned that the graph of a proportional relationship lies on a line through the origin. (Students should come to use and understand “the origin” to mean \((0,0)\).) In this lesson, they start to make connections between the graph and the context modeled by the proportional relationship, and between the graph and the equation for the proportional relationship. Given a graph, they think about what situation it might represent and learn the importance of being precise about saying which quantities are represented on each axis (MP6). They interpret the meaning of the point \((1,k)\) on the graph both in term of the constant of proportionality \(k\) in the equation \(y = kx\) and in terms of a constant rate in the context.
- Create the graph of a proportional relationship given only one pair of values, by drawing the line that connects the given point and (0, 0).
- Identify the constant of proportionality from the graph of a proportional relationship.
- Interpret (orally and in writing) points on the graph of a proportional relationship.
Let’s read stories from the graphs of proportional relationships.
- I can draw the graph of a proportional relationship given a single point on the graph (other than the origin).
- I can find the constant of proportionality from a graph.
- I understand the information given by graphs of proportional relationships that are made of up of points or a line.
The coordinate plane is a system for telling where points are. For example. point \(R\) is located at \((3, 2)\) on the coordinate plane, because it is three units to the right and two units up.
The origin is the point \((0,0)\) in the coordinate plane. This is where the horizontal axis and the vertical axis cross.