Linear Relationships Test Review

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

Back

The slope of a line is a measure of its steepness, represented as the ratio of the rise (change in y) over the run (change in x). It indicates the rate of change of the function.

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What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It is the value of y when x = 0.

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What is a nonlinear function?

Back

A nonlinear function is a function whose graph is not a straight line. It can be represented by equations that include exponents, roots, or other non-linear operations.

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What does it mean for a relation to be a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value). This means that no x-value is paired with more than one y-value.

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What is the formula for calculating slope?

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The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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What is the difference between a linear and a nonlinear graph?

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A linear graph forms a straight line, while a nonlinear graph can take various shapes, such as curves or parabolas.

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What is an example of a linear function?

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An example of a linear function is y = 2x + 3, which has a constant slope of 2.

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What is an example of a nonlinear function?

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An example of a nonlinear function is y = x^2, which forms a parabola.

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What does 'constant rate of change' mean?

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A constant rate of change means that the output (y-value) changes at a consistent rate for each unit change in the input (x-value), characteristic of linear functions.