Drawing Line Graphs
4A · Chapter 9 · Lesson 2 · MATH-4A-C09-L02
Learning goal. Choose scales, label axes, plot points and connect appropriate ordered measurements.
Before you begin
Recall: Grade 3A: picture and bar graphs, tables; 4A: data comparisons; Line Graphs. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Using the graph, calculate the signed change from Tue to Fri.
Show answer & reasoning
Read the two measurements: 21 − 13 = 8.
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 4. Subtract to get 15.
From the line graph below, read the number collected on Fri.
Show answer & reasoning
Read the plotted point above Fri on the vertical scale: 14.
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
To construct a line graph, put ordered categories or times on the horizontal axis and measured amounts on the vertical axis. Choose equal numeric intervals that reach the largest value. Plot each pair carefully and connect adjacent points only when that connection conveys change. Label the title and units so a reader can interpret the graph.
Model it: blank axes, plotted coordinates and an appropriate scale. 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
Construct a correctly labeled line graph for daily rainfall in millimeters: Mon: 7, Tue: 16, Wed: 13, Thu: 6, Fri: 7. State the highest value.
Choose a consistent axis scale from zero to at least 16; plot all five points in weekday order, connect adjacent points, and identify the maximum of 16.
Check your understanding 1
Construct a correctly labeled line graph for daily plant height in centimeters: Mon: 7, Tue: 12, Wed: 22, Thu: 17, Fri: 22. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 22; plot all five points in weekday order, connect adjacent points, and identify the maximum of 22.
Worked example 2
From the line graph below, read the number collected on Thu.
Read the plotted point above Thu on the vertical scale: 8.
Check your understanding 2
From the line graph below, read the number collected on Tue.
Show answer & reasoning
Read the plotted point above Tue on the vertical scale: 4.
Worked example 3
From the line graph below, read the number collected on Thu.
Read the plotted point above Thu 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: 17.
Guided practice
Construct a correctly labeled line graph for daily book checkouts: Mon: 18, Tue: 16, Wed: 7, Thu: 18, Fri: 9. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 18; plot all five points in weekday order, connect adjacent points, and identify the maximum of 18.
From the line graph below, read the number collected on Thu.
Show answer & reasoning
Read the plotted point above Thu on the vertical scale: 17.
From the line graph below, read the number collected on Fri.
Show answer & reasoning
Read the plotted point above Fri on the vertical scale: 10.
Construct a correctly labeled line graph for daily rainfall in millimeters: Mon: 21, Tue: 19, Wed: 12, Thu: 22, Fri: 23. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 23; plot all five points in weekday order, connect adjacent points, and identify the maximum of 23.
Using the graph, calculate the signed change from Thu to Fri.
Show answer & reasoning
Read the two measurements: 14 − 11 = 3.
Independent practice
From the line graph below, read the number collected on Tue.
Show answer & reasoning
Read the plotted point above Tue on the vertical scale: 12.
From the line graph below, read the number collected on Wed.
Show answer & reasoning
Read the plotted point above Wed on the vertical scale: 12.
Construct a correctly labeled line graph for daily book checkouts: Mon: 9, Tue: 20, Wed: 11, Thu: 23, Fri: 18. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 23; plot all five points in weekday order, connect adjacent points, and identify the maximum of 23.
Using the graph, calculate the signed change from Mon to Thu.
Show answer & reasoning
Read the two measurements: 15 − 19 = -4.
Construct a correctly labeled line graph for daily book checkouts: Mon: 16, Tue: 20, Wed: 18, Thu: 19, Fri: 22. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 22; plot all five points in weekday order, connect adjacent points, and identify the maximum of 22.
Construct a correctly labeled line graph for daily plant height in centimeters: Mon: 13, Tue: 15, Wed: 15, Thu: 22, Fri: 19. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 22; plot all five points in weekday order, connect adjacent points, and identify the maximum of 22.
From the line graph below, read the number collected on Mon.
Show answer & reasoning
Read the plotted point above Mon on the vertical scale: 20.
From the line graph below, read the number collected on Mon.
Show answer & reasoning
Read the plotted point above Mon on the vertical scale: 19.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student draws a line graph for daily readings using unequal vertical tick intervals labeled 0, 5, 20, 25. Explain why this can mislead.
Show answer & reasoning
The vertical axis must use a consistent numeric scale; unequal steps distort comparisons.
Construct a correctly labeled line graph for daily book checkouts: Mon: 13, Tue: 19, Wed: 18, Thu: 11, Fri: 11. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 19; plot all five points in weekday order, connect adjacent points, and identify the maximum of 19.
Exit check
Construct a correctly labeled line graph for daily rainfall in millimeters: Mon: 16, Tue: 19, Wed: 23, Thu: 20, Fri: 18. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 23; plot all five points in weekday order, connect adjacent points, and identify the maximum of 23.
Using the graph, calculate the signed change from Tue to Wed.
Show answer & reasoning
Read the two measurements: 21 − 18 = 3.
Construct a correctly labeled line graph for daily book checkouts: Mon: 10, Tue: 12, Wed: 7, Thu: 14, Fri: 9. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 14; plot all five points in weekday order, connect adjacent points, and identify the maximum of 14.