You can plot and read points on the coordinate plane. When the axes measure real things, like hours and dollars, each point tells a small story.
Key idea
Each axis has a name and a scale. A point $(x, y)$ pairs one value from the across axis with one value from the up axis. To read the story, say both values with their units.
Why it works
If you earn \$8 an hour, then 1 hour pairs with \$8, 2 hours with \$16, and so on. Each pair becomes a point: $(1, 8), (2, 16), (3, 24)$. The graph shows all the pairs at once, so you can read values, spot the pattern and predict the next point.
Worked examples
Worked example: Read a value
Use the graph. How much is earned in 4 hours?
- Find 4 on the across axis (hours).
- Go up to the point and read left: 32.
Answer: \$32
Worked example: What a point means
What does the point $(3, 24)$ mean?
- The first number is on the hours axis: 3 hours.
- The second number is on the dollars axis: \$24.
Answer: Working 3 hours earns \$24.
Worked example: Predict
If the pattern continues, how much is earned in 7 hours?
- Each hour adds \$8.
- From $(5, 40)$: $40 + 8 + 8 = 56$.
Answer: \$56
Common mistake
Reading the scale as 1, 2, 3 when it counts by 8s, or swapping which number goes with which axis. Check the axis names and the step between grid lines before you read a value.