Linear or Nonlinear

Front

What is a linear equation?

Back

An equation that graphs to a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear equation?

Back

An equation that does not graph to a straight line, which can include curves, circles, and other shapes.

Front

Give an example of a linear equation.

Back

y = 2x + 3 is a linear equation.

Front

Give an example of a nonlinear equation.

Back

y = x^2 + 2 is a nonlinear equation.

Front

What does the slope of a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

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

How can you determine if an equation is linear or nonlinear?

Back

Check if the highest power of the variable is 1 (linear) or greater than 1 (nonlinear).

Front

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

Back

Ax + By = C, where A, B, and C are constants.

Front

What is a characteristic of a nonlinear function?

Back

Nonlinear functions can have curves, bends, or multiple outputs for a single input.

Front

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

Back

A linear function has a constant rate of change, while a nonlinear function does not.