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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.F.A.3

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.

Tags

CCSS.8.F.A.3

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.

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSF-LE.A.1B

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'.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSF-LE.A.1B

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).

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.F.A.3