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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from a graph?

Back

A linear function will produce a straight line when graphed.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Tags

CCSS.8.F.A.3

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.

Tags

CCSS.8.F.A.3

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.

Tags

CCSS.8.EE.B.5