Linear or Nonlinear

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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 equation?

Back

A nonlinear equation is an equation that does not form a straight line when graphed. It can include quadratic, cubic, exponential, and other types of equations that have variables raised to a power other than one.

Front

How can you identify a linear equation from its graph?

Back

A linear equation will produce a graph that is a straight line, with a constant slope throughout.

Front

What are the characteristics of a linear equation?

Back

Characteristics of a linear equation include: 1) It has a degree of 1, 2) It can be written in the form Ax + By = C, 3) It has a constant rate of change.

Front

What are some examples of linear equations?

Back

Examples of linear equations include: 1) y = 2x + 3, 2) 3x - 4y = 12, 3) y = -5.

Front

What are some examples of nonlinear equations?

Back

Examples of nonlinear equations include: 1) y = x^2 (quadratic), 2) y = e^x (exponential), 3) y = sin(x) (trigonometric).

Front

What is the slope of a linear equation?

Back

The slope of a linear equation is a measure of the steepness of the line, calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

Can a linear equation have more than one variable?

Back

Yes, a linear equation can have multiple variables, such as in the form Ax + By + Cz = D, where A, B, C, and D are constants.

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function has a variable rate of change and graphs as a curve.