Common Core Standards: Math
Ratios and Proportional Relationships 7.RP.A.2.d
2d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
When we graph a proportional relationship, the trickiest part is making sure we've got the right variables. Emphasize to your students that each point on the graph represents the value of the independent variable (y) when the dependent variable (x) is at a particular value (and that this relationship will always still reflect the ratio/unit rate).
This standard expects them to understand and clearly tell you exactly what these points mean for any given situation. For instance, if Claude makes $10 per hour at his job washing horses, the point (x, y) shows that he makes y dollars after he works x hours. Your students should know that this is true no matter how much or how little he works—if he washes horses for 20 straight hours, he'll have a sore back but also $200 in his pocket, since the graph passes through the point (20, 200).
Students should also be able to explain why Claude's unit rate (10 bucks an hour) is represented by the point (1, 10)—10 dollars for 1 hour's work—and why working zero hours brings us to the point (0, 0), which means he's still broke. Though we can't really blame him, since getting kicked in the face by a giant hoof is a pretty huge occupational hazard.