2023 Fall Semester Exam Review #2

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What is a linear function?

Back

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What does it mean for a system of linear equations to have one solution?

Back

A system of linear equations has one solution when the lines represented by the equations intersect at exactly one point.

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How do you determine if a point is a solution to a system of equations?

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To determine if a point is a solution, substitute the x and y values of the point into both equations. If both equations are satisfied, the point is a solution.

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

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What is the significance of the y-intercept in a linear function?

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

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What does it mean if two linear equations are parallel?

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If two linear equations are parallel, they have the same slope but different y-intercepts, meaning they will never intersect.

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What is the difference between a consistent and inconsistent system of equations?

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A consistent system has at least one solution, while an inconsistent system has no solutions.

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How can you tell if a function is nonlinear?

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A function is nonlinear if its graph is not a straight line, which can be identified by the presence of exponents other than 1, square roots, or other non-linear transformations.