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8th Grade · 8.F.B.5

Interpreting graphs in 8th grade math

Interpreting graphs means reading the story a graph tells: when something goes up, goes down or stays the same, and whether it changes at a steady speed. In 8th grade, your child describes the graph of a function in words, without needing exact numbers. Your child also sketches a graph from a story, such as a fish tank that is filled and then drained.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

What it means, in plain words

In 8th grade, interpreting graphs is about the shape of a function more than its exact values. Your child reads the graph from left to right, the way time usually moves. Increasing and decreasing functions are named by that direction. Where the line goes up, the function is increasing: the output grows as the input grows. Where it goes down, the function is decreasing. A flat part means the output stays the same.

Steepness tells the speed. A straight part means the output changes at a steady rate, so that part is linear. A curved part means the rate keeps changing, so that part is nonlinear. A curve that gets steeper shows something speeding up, and a curve that flattens out shows it slowing down.

The skill also runs the other way. Graphing functions from a description means turning a story into a sketch. For a fish tank that is filled, left full for a while and then drained, the sketch rises, stays flat and then falls. Your child does not need a scale or exact numbers here, only the right shapes in the right order.

Your child should be able to:

  • Say where a graph is increasing, decreasing or flat
  • Tell which parts of a graph are linear (straight) and which are nonlinear (curved)
  • Describe what a graph shows as a story, for example "the water rose quickly, then slowly"
  • Sketch a graph from a story told in words

Example

A graph shows a car's distance from home over 30 minutes. It rises in a straight line for 10 minutes, stays flat for 5 minutes, then falls in a straight line back to 0 at 30 minutes. What happened on the trip?

  1. Rising part: the car moves away from home. The line is straight, so the speed is steady.
  2. Flat part: the distance does not change, so the car is stopped for 5 minutes.
  3. Falling part: the car drives back home. It starts back at 10+5=1510 + 5 = 15 minutes and arrives at 30 minutes, so the drive home takes 30−15=1530 - 15 = 15 minutes.
  4. The car drove away for 10 minutes, stopped for 5 minutes, then took 15 minutes to drive home.

Example

Sketch a graph of a plant's height over a month: it does not grow in the first week, then grows slowly, then grows quickly.

  1. Start with a flat part for the first week, because the height stays the same.
  2. Next, draw a gentle rise for the slow growth.
  3. Finish with a steeper rise for the fast growth.
  4. The sketch is flat, then rises gently, then rises steeply. It needs no numbers.

Where children usually get stuck

  • Your child sees a graph of a car's distance from home that goes up and then down, and says the car drove up a hill and down the other side.

    The graph looks like a picture of a hill. The child reads the shape as the path of the car instead of reading what the vertical axis measures.

    What helps. Before describing any graph, have your child read both axis labels out loud and start a sentence with them: "As time goes on, the distance from home..."

  • Asked to sketch "grows slowly, then quickly", your child draws a steep part first and a gentle part second.

    A steep hill is slow to climb, so steep feels like slow. On a graph, steep means the output changes a lot in a short time, which is fast.

    What helps. Take one step to the right on each part and compare. The part that rises more in the same step is the faster one.

  • Your child says the function is decreasing wherever the line is below the horizontal axis.

    "Low" and "going down" get mixed up. Decreasing is about direction, the line falling from left to right, not about where the line sits on the page.

    What helps. Have your child trace the line with a finger from left to right and say "up", "down" or "flat" for each part. Where the line sits does not matter for this question.

Try four practice questions

Real 8th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    Which graphs could show the water level in a fish tank that was filled to a set level, held steady, and then drained? Select all that apply.
    A
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    B
    2468102468100xy
    C
    2468102468100xy
    D
    2468102468100xy
    Show the answer and how to solve it

    Graph A and Graph B are correct. Both graphs rise, stay flat, and then fall, matching every part of the fill-hold-drain story.

    1. 1Translate the story into the order of changes: increase → flat → decrease.
    2. 2The water was held steady, so the middle segment must be horizontal. Any graph whose middle segment is still rising or falling cannot show the water being kept at a constant level.
    3. 3Graph A and Graph B both rise, hold flat, and then fall, so they are both correct. Graph C keeps rising in the middle with no flat section. Graph D rises and has a flat middle but then goes up again at the end instead of falling.

    Common mistake. A common mistake is checking only that the graph goes up and then down without verifying that the middle segment must be flat to show the water being held at a steady level.

    The idea underneath. A qualitative story fixes the order and type of changes even when it does not fix exact coordinates.

  2. 2On level
    Zara was asked to sketch a graph that rises and then falls, making one peak. Look at Zara's sketch. Which evaluation is best?
    -6-5-4-3-2-1123456-4-3-2-112340xy
    A
    The sketch is correct.
    B
    The sketch shows the opposite turning type.
    C
    The sketch has no turning point.
    D
    The sketch has more than one turning point.
    Show the answer and how to solve it

    The best evaluation is: The sketch has more than one turning point. Zara's sketch rises, falls, and then rises again, giving it two turning points instead of one.

    1. 1Read Zara's sketch from left to right.
    2. 2The graph rises, then falls, then rises again.
    3. 3The first fall does make one peak. But Zara's sketch does not stop there—the last segment rises again, so the graph changes direction a second time.
    4. 4A graph with one peak should change direction exactly once. Zara's sketch changes direction twice, so it has more than one turning point.

    Common mistake. A common mistake is choosing 'The sketch is correct' because Zara's graph does rise and then fall at first. Be sure to trace the entire sketch all the way to the right so you do not miss the second direction change.

    The idea underneath. To judge a turning-point sketch, follow the whole graph from left to right and count each time the direction changes between rising and falling.

  3. 3On level
    Look at the graph. Match each description to the best label. One label will not be used.
    xy
    Connect each item on the left to its match on the right.
    Description
    Label
    decreases, then increases, then stays constant
    stays constant, then increases, then decreases
    decreases, then stays constant
    Left out one phase
    Correct
    Added a constant phase that is not on the graph
    Reversed the left-to-right order

    Use Tab to navigate between items. Click or tap a card to select it, then click or tap a card on the opposite side to create a match. You can also drag a card or its connector dot to a card on the opposite side.

    Show the answer and how to solve it

    Description 1 matches Correct, description 2 matches Reversed the left-to-right order, and description 3 matches Left out one phase. The unused label is Added a constant phase that is not on the graph.

    1. 1Read the graph from left to right. It falls first, then rises, then levels off.
    2. 2The correct phase order is: decreases, then increases, then stays constant.
    3. 3Description 1 says 'decreases, then increases, then stays constant.' That matches the graph exactly, so its label is Correct.
    4. 4Description 2 says 'stays constant, then increases, then decreases.' This lists the phases in reverse order from right to left, so its label is Reversed the left-to-right order.
    5. 5Description 3 says 'decreases, then stays constant.' It skips the rising middle section entirely, so its label is Left out one phase.
    6. 6The label 'Added a constant phase that is not on the graph' is not used because none of the descriptions includes an extra flat part that the graph does not show.

    Common mistake. A common mistake is to skip the middle increasing segment and pair the initial drop directly with the final flat part. The rising portion is its own phase and must appear between the decreasing and constant phases.

    The idea underneath. A qualitative graph description must list every change in behavior in the exact order the graph shows from left to right.

  4. 4Stretch
    Select all x-values where the graph crosses the x-axis.
    -7-6-5-4-3-2-1123456-3-2-112340xy
    A
    -3
    B
    -1
    C
    1
    D
    3
    E
    4
    Show the answer and how to solve it

    Select -3, 1, and 4 because those are the only x-values where the graph crosses the x-axis.

    1. 1Look along the x-axis for every point where the graph sits directly on it. Any point on the x-axis has y = 0.
    2. 2Starting on the left, the segment from (-6, 3) descends and meets the x-axis exactly at (-3, 0). The segment before has y = 3 > 0 and the segment after drops to y = -2 < 0, confirming this is a genuine crossing. First zero: x = -3.
    3. 3The graph dips to (-1, -2) and then the segment from (-1, -2) to (3, 2) travels from below the x-axis to above it. The segment spans 4 units in x and 4 units in y, so it crosses halfway through at x=−1+2=1x = -1 + 2 = 1. Second zero: x = 1.
    4. 4After peaking at (3, 2), the segment from (3, 2) to (5, -2) goes from above the x-axis to below it. It crosses halfway along the segment, at (4, 0). The third zero is x = 4.
    5. 5The correct selections are -3, 1, and 4. The graph is at y = -2 when x = -1 and at y = 2 when x = 3, so those turning points are not zeros.

    Common mistake. A common mistake is choosing x = 3 because the graph peaks there at a visible turning point. However, the point (3, 2) is 2 units above the x-axis.

    The idea underneath. A zero is an input value, so you read the x-coordinate of each point where the graph has y = 0.