Linear or Nonlinear

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written 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.

Front

Identify the following equation as linear or nonlinear: y = 2x + 3.

Back

Linear

Front

Identify the following equation as linear or nonlinear: y = x^2 + 2.

Back

Nonlinear

Front

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

Back

The general form is Ax + By = C, where A, B, and C are constants.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a linear equation and its graph is a straight line.

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 b in the equation y = mx + b.

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^3 - 4x.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and graph as curves.