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What is a linear equation?

Back

A linear equation is an equation that can be expressed in the form ax + b = 0, where a and b are constants, and x is a variable. The graph of a linear equation is a straight line.

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What is a nonlinear equation?

Back

A nonlinear equation is an equation that does not form a straight line when graphed. It can include variables raised to a power greater than one, products of variables, or other non-linear terms.

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How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change, meaning the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

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What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

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What does the slope of a linear function represent?

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The slope of a linear function represents the rate of change of the function; it indicates how much y changes for a unit change in x.

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What is the y-intercept of a linear function?

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The y-intercept of a linear function is the point where the graph intersects the y-axis, represented by the value of y when x = 0.

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Can a linear function have a slope of zero?

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Yes, a linear function can have a slope of zero, which means it is a horizontal line and the output value (y) remains constant regardless of the input value (x).

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola and does not form a straight line.

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How do you determine if a function is linear or nonlinear from its graph?

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A function is linear if its graph is a straight line. If the graph curves or has any bends, it is nonlinear.

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What is the general form of a linear equation in two variables?

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The general form of a linear equation in two variables is Ax + By + C = 0, where A, B, and C are constants.