Grade 7 · Unit 1 · Lesson 6 · part 3 of 5
Two special points, and two tricky ones
Two points on every proportional graph are special.
Two special points, and two tricky ones
Two points on every proportional graph are special.
The origin, (0, 0)
Zero in gives zero out. It is on every proportional graph, because nothing of one amount always means nothing of the other. No mowing, no money.
The unit-rate point, (1, r)
At an input of 1, the output is the unit rate. On Jordan's graph that is (1, 8). So you can read r right off the graph: go over to 1, then up to the line.
Now try two more. A point between the grid lines, like (2.5, 20): in 2.5 hours, you get 20 dollars. It is on the line, because 8 × 2.5 = 20, and hours can be split, so it is a real point of the story. And a point that is not on the line, like (4, 30). What does that mean? It is not part of Jordan's job at all. 4 hours earns 8 × 4 = $32, not $30. A point off the line is a pair that the relationship does not make.
Tap points on Jordan's graph below, or type an x, and say what each one means. Try (3, 24), the origin, (1, 8), and 2.5. Then tap the navy dot at (4, 30), which is off the line.