Functions (linear)

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What is a linear function?

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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 a nonlinear function?

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A nonlinear function is a function that does not create a straight line when graphed. Examples include quadratic functions, exponential functions, and any function that involves variables raised to a power other than one.

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What does it mean for a function to be proportional?

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A function is proportional if it can be expressed in the form y = kx, where k is a constant. In a proportional relationship, the ratio of y to x is constant.

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What does it mean for a function to be nonproportional?

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A function is nonproportional if it does not maintain a constant ratio between y and x. This means that as x changes, the ratio of y to x changes.

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What is the slope of a linear function?

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The slope of a linear function is the rate at which y changes with respect to x. It is represented by the letter m in the equation y = mx + b.

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What is the y-intercept of a linear function?

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The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by the letter b in the equation y = mx + b.

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How can you identify a linear function from its graph?

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A linear function can be identified by its straight-line graph. If the graph curves or bends, it is not a linear function.

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What is an example of a linear equation?

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An example of a linear equation is y = 2x + 3.

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What is an example of a nonlinear equation?

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An example of a nonlinear equation is y = x^2 + 2.

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What is the difference between linear and nonlinear graphs?

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Linear graphs are straight lines, while nonlinear graphs can be curves or other shapes that do not form a straight line.