Lesson 2: Analyze Graphs of Relationships Between Two Variables6.AT.11

I can…

I can use a table and a graph to determine and analyze the relationship between two variable quantities.

Key words

• graph — A picture on a coordinate plane that shows how two quantities are related.
• table of values — A list of matched pairs of values that shows a relationship using numbers.
• ordered pair — Two numbers written as (x, y) that name one point on a graph. The independent variable comes first.
• axis — One of the two number lines that frame a graph. Each axis is labeled with a quantity from the problem.
• coordinates — The numbers in an ordered pair that tell how far to move along each axis to reach a point.
• Rate of change — How much y changes each time x goes up by one.
• Origin — The point (0, 0) where the two axes meet.

Steps

1. Each ticket costs $45, so the total cost is 45 times the number of tickets: 1 ticket is $45, 2 tickets are $90, 3 tickets are $135.
2. The number of tickets is the independent variable, so it goes first in each ordered pair: (1, 45), (2, 90), (3, 135).
3. I label one axis 'Number of tickets' and the other 'Total cost ($)', then plot each pair as a point.
4. The points rise to the right: as the number of tickets increases, the total cost increases.

Try it

Movie tickets cost $12 each. A graph shows the number of tickets on the x-axis and the total cost in dollars on the y-axis. What does the point (4, 48) represent?

Check your answer

4 tickets cost a total of $48

The independent variable — number of tickets — comes first in the ordered pair, and 4 × $12 = $48, so the point pairs 4 tickets with a total cost of $48.

Sentence starter

I know ___ because ___.

Goal: I can describe what a point on a graph represents using the words ordered pair, axis, and coordinates.