Line Graphs
4A · Chapter 9 · Lesson 1 · MATH-4A-C09-L01
Learning goal. Interpret values and changes on a labeled line graph with appropriate intervals.
Before you begin
Recall: Grade 3A: picture and bar graphs, tables; 4A: data comparisons. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
A shop starts with 9 items and sells 1/3. It then sells 1/2 of what remains. How many items remain?
Show answer & reasoning
First 3 sell, leaving 6. Taking 1/2 of that remainder removes 3, so 3 remain.
A shop starts with 20 items and sells 6/10. It then sells 1/2 of what remains. How many items remain?
Show answer & reasoning
First 12 sell, leaving 8. Taking 1/2 of that remainder removes 4, so 4 remain.
A shop starts with 12 items and sells 2/4. It then sells 1/2 of what remains. How many items remain?
Show answer & reasoning
First 6 sell, leaving 6. Taking 1/2 of that remainder removes 3, so 3 remain.
Key vocabulary
- line graph
- ordered measurements connected to display change
- line plot
- frequency display using marks above values
- axis
- reference line for labels or quantities
- scale
- equal numeric intervals on an axis
Understand the concept
A line graph shows how a measured quantity changes across ordered positions such as days. Read values using both axis labels and the marked numeric scale. Changes between two points are found by subtraction, not by counting spaces when the scale skips numbers. Only connect points when their order forms a meaningful progression.
Model it: labeled axes, scaled grid and ordered measured points. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
From the line graph below, read the number collected on Wed.
Read the plotted point above Wed on the vertical scale: 12.
Check your understanding 1
From the line graph below, read the number collected on Tue.
Show answer & reasoning
Read the plotted point above Tue on the vertical scale: 20.
Worked example 2
From the line graph below, read the number collected on Wed.
Read the plotted point above Wed on the vertical scale: 16.
Check your understanding 2
From the line graph below, read the number collected on Wed.
Show answer & reasoning
Read the plotted point above Wed on the vertical scale: 17.
Worked example 3
From the line graph below, read the number collected on Mon.
Read the plotted point above Mon on the vertical scale: 6.
Check your understanding 3
From the line graph below, read the number collected on Thu.
Show answer & reasoning
Read the plotted point above Thu on the vertical scale: 9.
Guided practice
From the line graph below, read the number collected on Thu.
Show answer & reasoning
Read the plotted point above Thu on the vertical scale: 21.
From the line graph below, read the number collected on Mon.
Show answer & reasoning
Read the plotted point above Mon on the vertical scale: 11.
From the line graph below, read the number collected on Wed.
Show answer & reasoning
Read the plotted point above Wed on the vertical scale: 13.
Using the graph, calculate the signed change from Tue to Thu.
Show answer & reasoning
Read the two measurements: 16 − 4 = 12.
Using the graph, calculate the signed change from Thu to Fri.
Show answer & reasoning
Read the two measurements: 17 − 17 = 0.
Independent practice
From the line graph below, read the number collected on Mon.
Show answer & reasoning
Read the plotted point above Mon on the vertical scale: 9.
From the line graph below, read the number collected on Fri.
Show answer & reasoning
Read the plotted point above Fri on the vertical scale: 19.
Using the graph, calculate the signed change from Mon to Fri.
Show answer & reasoning
Read the two measurements: 16 − 21 = -5.
Using the graph, calculate the signed change from Mon to Thu.
Show answer & reasoning
Read the two measurements: 4 − 15 = -11.
What is the range (greatest value minus least value) of the graph?
Show answer & reasoning
The largest plotted value is 23 and the smallest is 12. Subtract to get 11.
From the line graph below, read the number collected on Fri.
Show answer & reasoning
Read the plotted point above Fri on the vertical scale: 16.
From the line graph below, read the number collected on Tue.
Show answer & reasoning
Read the plotted point above Tue on the vertical scale: 9.
From the line graph below, read the number collected on Thu.
Show answer & reasoning
Read the plotted point above Thu on the vertical scale: 20.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A line graph uses a scale marked at 10 and 40. A student assumes halfway between tick marks must mean one more unit. Explain why that method is unreliable.
Show answer & reasoning
A point halfway between labeled values must represent their arithmetic mean, not a count of printed tick marks.
What is the range (greatest value minus least value) of the graph?
Show answer & reasoning
The largest plotted value is 19 and the smallest is 7. Subtract to get 12.
Exit check
Using the graph, calculate the signed change from Mon to Thu.
Show answer & reasoning
Read the two measurements: 20 − 14 = 6.
Using the graph, calculate the signed change from Mon to Fri.
Show answer & reasoning
Read the two measurements: 16 − 15 = 1.
What is the range (greatest value minus least value) of the graph?
Show answer & reasoning
The largest plotted value is 23 and the smallest is 5. Subtract to get 18.