Linear/Nonlinear/Equations from tables

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It has a constant rate of change and 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 graph to a straight line. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

Front

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

Back

To determine if a function is linear or nonlinear from a table, check if the differences between consecutive y-values are constant for equal intervals of x-values. If they are constant, the function is linear; if not, it is nonlinear.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which represents how much the y-value changes for a unit change in the x-value.

Front

What does a constant slope indicate about a function?

Back

A constant slope indicates that the function is linear, meaning it has a consistent rate of change.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x). It is often represented by the letter 'm'.

Front

If a table shows the following values: (1, 2), (2, 4), (3, 6), what is the rate of change?

Back

The rate of change is 2, as for every increase of 1 in x, y increases by 2.

Front

What does it mean if a function has a slope that is not constant?

Back

If a function has a slope that is not constant, it indicates that the function is nonlinear, meaning the rate of change varies.

Front

How can you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1).

Front

What is an example of a nonlinear function?

Back

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