Linear vs Non Linear Equations

Front

What is a linear equation?

Back

An equation that can be written in the form y = mx + b, where m and b are constants.

Front

What is a nonlinear equation?

Back

An equation that cannot be written in the form y = mx + b, often involving exponents, roots, or other non-linear terms.

Front

How can you identify a linear function from a graph?

Back

A linear function will produce a straight line when graphed.

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 does the slope (m) represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis.

Front

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

Back

Linear graphs are straight lines, while nonlinear graphs can be curves or other shapes.

Front

What are some common forms of nonlinear equations?

Back

Quadratic equations (y = ax^2 + bx + c), exponential equations (y = a * b^x), and trigonometric equations.

Front

What is the significance of exponents in identifying nonlinear equations?

Back

Exponents greater than 1 indicate a nonlinear relationship.

Front

Can a linear equation have a slope of zero?

Back

Yes, a linear equation can have a slope of zero, which means it is a horizontal line.