Linear/Nonlinear/Equations from tables

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Its rate of change is not constant, and it can take various forms such as curves or circles.

Front

How can you determine if a function is linear or nonlinear from a table of values?

Back

If the differences between consecutive y-values are constant for equal changes in x-values, the function is linear. If the differences vary, the function is nonlinear.

Front

What does the term 'slope' refer to in a linear equation?

Back

The slope refers to the steepness of the line, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

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What is an example of a linear equation?

Back

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

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What is an example of a nonlinear equation?

Back

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

Front

What does it mean if a table shows a constant rate of change?

Back

A constant rate of change indicates that the relationship between x and y is linear.

Front

What is the significance of the start number in a table of values?

Back

The start number (or initial value) is the y-value when x is at its minimum or starting point, often indicating the starting condition of the function.

Front

How can you identify a nonlinear relationship from a graph?

Back

A nonlinear relationship can be identified by a curve or any shape that is not a straight line on the graph.