Linear vs Non Linear Equations

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a non-linear equation?

Back

A non-linear equation is an equation that does not form a straight line when graphed. Examples include quadratic equations, exponential equations, and trigonometric equations.

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 and A and B are not both zero.

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). It indicates how steep the line is.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. The differences in y-values divided by the differences in x-values will be the same.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

What is the difference between a linear and a non-linear graph?

Back

A linear graph is a straight line, while a non-linear graph can be curved or have bends, indicating a variable rate of change.

Tags

CCSS.8.F.A.3

Front

What is a quadratic equation?

Back

A quadratic equation is a type of non-linear equation that can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you determine if a function is linear or non-linear from its graph?

Back

If the graph is a straight line, the function is linear. If the graph is curved or has bends, the function is non-linear.

Tags

CCSS.8.F.A.3