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Plot and Read Line Graphs with Negative Values
Learn to plot temperature-style data with negative values on a line graph and read values accurately from a labeled axis crossing zero.
Free lesson
Four exercises
Worked answers
Algebra and Function Practice
Line graphs often show temperatures that fall below zero, so the vertical axis must include negative numbers. This lesson teaches you to set up an axis that crosses zero, plot points with negative values, and read values from the graph. You will use a simple convention: place the center of each marker exactly on the grid intersection. Marker size and style may vary as long as the center is unambiguous. All numerical examples are hypothetical and chosen for easy checking.
Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.
Setting Up an Axis That Crosses Zero
A line graph with negative values needs a vertical axis that includes both positive and negative numbers. Choose a scale that fits your data, such as counting by 2s or 5s, and mark zero clearly. The horizontal axis usually shows time or categories, and the vertical axis shows the measured value.
Label every tick mark you use, or label enough that any point can be read. Keep units consistent, for example degrees Celsius for all temperatures. If your data ranges from -8 to 6, a scale from -10 to 10 with steps of 2 works well.
- List your data values and find the lowest and highest numbers.
- Choose a vertical scale that includes zero and covers both extremes with a little room.
- Draw and label the vertical axis, marking zero with a clear line.
- Draw and label the horizontal axis for time or categories.
- Check that each grid line represents the same amount.
Plotting Points with Negative Values
To plot a point, start at zero on the vertical axis. Move up for positive values and down for negative values. Then move right along the horizontal axis to the correct time or category. Place the point exactly where the two positions meet.
Use a consistent marker size. Place the center of each marker exactly on the intended grid intersection. Different handwriting or marker styles are acceptable if the center is clear.
- Find the time or category on the horizontal axis.
- From zero on the vertical axis, count up or down to the value.
- Mark the point at the intersection of the two positions.
- Label the point with its value if space allows.
- Repeat for each data pair, then connect the points in order with straight line segments.
Reading Values from the Graph
To read a value, locate the point on the line graph, then follow a horizontal line to the vertical axis. If the point is below zero, the value is negative. Read to the nearest labeled tick or estimate between ticks if the scale allows.
When comparing two points, note whether the line goes up or down. A line going down from a positive value to a negative value shows a decrease that crosses zero.
- Find the correct point on the horizontal axis.
- Move vertically to the plotted point or line.
- Move horizontally to the vertical axis.
- Read the number, including a negative sign if below zero.
- State the value with its unit.
Checking Your Work
After plotting, check each point against the data table. Count grid steps from zero to confirm the value. For reading questions, verify by counting steps back from the axis to the point.
A quick arithmetic check: if two points are at -4 and 2, the vertical difference is 6 units. Count the grid steps between them to confirm your scale is consistent.
- Compare each plotted point with its table value.
- Count grid steps from zero to each point.
- Check that connected segments follow the data order.
- Re-read each answer and confirm the sign and unit.
Worked example
A table shows temperatures at four times: 8:00 = -6, 10:00 = -2, 12:00 = 3, 14:00 = 1 (degrees Celsius). Plot these on a line graph with a vertical axis from -8 to 4 in steps of 2, then read the value at 10:00.
Worked answer
Plot points at (8:00, -6), (10:00, -2), (12:00, 3), and (14:00, 1). Connect them in order. Reading at 10:00 gives -2 degrees Celsius.
Four practice exercises
Exercise 1
Plot these values on a line graph with a vertical axis from -6 to 6 in steps of 1: Monday = -4, Tuesday = 0, Wednesday = 5, Thursday = -1. Then read the value for Thursday.
Show answer and check
Thursday = -1.
Why: Start at zero, move down 1 unit for Thursday, and mark the point. Reading back to the axis gives -1.
Check: Count grid steps from zero down toward the Thursday point. On a scale of 1 per grid line, -1 is exactly one grid line below zero, so confirm the point sits on that line and read it as -1.
Exercise 2
A graph shows points at (1, -3), (2, 2), (3, -5), and (4, 0). Describe where each point lies relative to zero and state which point is lowest.
Show answer and check
Point (1, -3) is below zero; (2, 2) is above zero; (3, -5) is below zero; (4, 0) is on zero. The lowest point is (3, -5).
Why: Negative second coordinates lie below zero, positive above, and zero on the axis. The most negative value is lowest.
Check: Compare the second coordinates: -3, 2, -5, 0. The smallest is -5, so (3, -5) is lowest.
Exercise 3
Using a vertical axis from -10 to 10 in steps of 5, plot: 6:00 = -8, 9:00 = -3, 12:00 = 7, 15:00 = 2. Read the value at 9:00 and state whether the line rises or falls from 6:00 to 9:00.
Show answer and check
Value at 9:00 is -3. The line rises from -8 to -3.
Why: Plot each point by moving up or down from zero. From -8 to -3 the value increases by 5, so the line goes upward.
Check: Count steps: -8 is below zero, -3 is closer to zero, so the segment slopes upward. Confirm -3 is three units below zero.
Exercise 4
A line graph has points at (A, -2), (B, 4), (C, -6), and (D, 1). Without drawing, list the points in order from lowest to highest value, and explain how the graph would cross zero between B and C.
Show answer and check
Order: C (-6), A (-2), D (1), B (4). Between B (4) and C (-6) the line goes from positive to negative, so it crosses zero.
Why: Compare values directly. A segment from a positive to a negative value must pass through zero.
Check: Sort the values: -6 < -2 < 1 < 4. Check that B is positive and C is negative, so zero lies between them.
Common mistakes
- Starting the vertical axis at zero and only going upward, so negative values cannot be plotted. Extend the axis below zero and label negative tick marks before plotting.
- Plotting a negative value above zero because the negative sign is ignored. Always move downward from zero for negative values and check the sign after plotting.
- Using uneven grid steps, such as counting by 2 then by 5. Choose one consistent step for the whole axis and label each tick.
- Reading a point below zero as positive. Follow the horizontal line to the axis and include the negative sign when the point is below zero.
Self-check rubric
- Vertical axis includes zero and is labeled with a consistent scale.
- All four points are plotted at the correct grid intersections, with negative values below zero.
- Points are connected in the correct time order.
- Reading answers include the correct sign and unit.
- Marker placement is clear: the center of each marker sits on the correct grid intersection, with acceptable style variation.
Questions and answers
Do I always need to show zero on the vertical axis?
Yes, when data includes negative values, zero must be shown so the sign of each value is clear.
Can I use different marker styles for points?
Yes, as long as the center of each marker sits exactly on the correct grid intersection. Marker size and style may vary.
How do I choose a scale?
Pick a step that divides evenly into your data range and keeps the graph readable, such as 2 or 5 units per grid line.
What if a value falls between two grid lines?
Estimate the position between the lines and state that it is an estimate, or adjust the scale so the value lands on a line.