Linear vs Non-Linear

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 function?

Back

A non-linear function is a function that does not form a straight line when graphed. It can include quadratic, exponential, logarithmic, and other types of functions.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear equation from its standard form?

Back

A linear equation in standard form is typically written as Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation y = mx + b. It indicates the change in y for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by 'b' in the equation y = mx + b.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line and the output value (y) remains constant regardless of the input value (x).

Tags

CCSS.8.EE.B.5

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

If the graph of the function is a straight line, it is linear. If the graph curves or has any bends, it is non-linear.

Tags

CCSS.8.F.A.3

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and the position of the line on the graph. The coefficient of x determines the slope, while the constant term affects the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of the graph that satisfies the inequality, often shown with a shaded area.

Tags

CCSS.HSA.REI.D.12