Graphing Data

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Variable Noun

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[vair-ee-uh-buhl]

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Variable

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Any factor, trait, or condition that can exist in differing amounts or types during an experimental investigation.

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Example: This diagram shows an experiment where fertilizer (the independent variable, which is changed on purpose) affects plant growth (the dependent variable, which is measured).

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Independent Variable Noun

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[in-di-pen-duhnt vair-ee-uh-buhl]

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Independent Variable

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The factor that is intentionally changed or manipulated by the investigator to observe its effect in an experiment.

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Example: The independent variable is the one factor a scientist changes on purpose. Here, adding fertilizer is the independent variable to test its effect on plant growth.

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Dependent Variable Noun

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[dee-pen-duhnt vair-ee-uh-buhl]

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Dependent Variable

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The factor that is measured or observed in an experiment to see how it is affected by the independent variable.

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Example: The amount of plant growth is the dependent variable because it is the outcome that is measured and depends on the change made in the experiment (adding fertilizer).

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Line of Best Fit Noun

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[layn uhv best fit]

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Line of Best Fit

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A straight line or curve drawn through the center of a group of data points on a scatter plot.

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Example: This scatter plot shows data points for arm span and height. The 'Line of Best Fit' is the straight line drawn through the data that best represents the general trend.

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Linear Relationship Noun

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[lin-ee-er ri-ley-shuhn-ship]

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Linear Relationship

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A relationship between two variables that, when graphed on a coordinate plane, forms a straight line.

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Example: This graph shows that as the number of sides of a polygon increases, the number of angles increases by the same amount, forming a straight line.

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Slope Noun

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[slohp]

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Slope

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A measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change.

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Example: This graph shows that slope is the steepness of a line, calculated by dividing the vertical change (rise) by the horizontal change (run).

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y-intercept Noun

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[wai-in-ter-sept]

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y-intercept

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The point on a graph where a line or curve crosses the vertical axis, representing the value when x is zero.

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Example: This graph shows that the y-intercept is the point where a line crosses the vertical y-axis, which always has an x-coordinate of zero.

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Quadratic Relationship Noun

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[kwah-drat-ik ri-ley-shuhn-ship]

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Quadratic Relationship

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A mathematical relationship where one variable depends on the square of another, typically forming a parabola when graphed.

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Example: This image shows a table of x and y values and their corresponding graph, which forms a U-shaped curve (a parabola), a key feature of a quadratic relationship.

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Inverse Relationship Noun

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[in-vurs ri-ley-shuhn-ship]

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Inverse Relationship

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A relationship where as one variable increases, the other variable decreases, often forming a hyperbolic curve when graphed.

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Example: This seesaw shows an inverse relationship; as one side goes up (representing an increase in one variable), the other side goes down (a decrease).

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Extrapolate Verb

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[ik-strap-uh-leyt]

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Extrapolate

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To estimate a value by extending a known sequence or trend beyond the area for which data is available.

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Example: This graph shows how to extrapolate by extending the 'Line of Best Fit' beyond the known data points (blue dots) to predict unknown values (red circles).