Characteristics of Linear Functions

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 f(x) = 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 does the slope (m) of a linear function represent?

Back

The slope (m) of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept of a linear equation, set y = 0 and solve for x.

Front

What is the significance of the y-intercept in a linear function?

Back

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

Front

What does it mean for a function to be positive?

Back

A function is positive when its output values (y-values) are greater than zero for a given range of x-values.

Tags

CCSS.HSF.LE.B.5

Front

How can you determine where a linear function is increasing or decreasing?

Back

A linear function is increasing when the slope (m) is positive and decreasing when the slope is negative.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

What does it mean for a function to approach infinity as x approaches negative infinity?

Back

If a function approaches infinity as x approaches negative infinity, it means that the function's values increase without bound as x decreases.

Tags

CCSS.HSF-IF.C.7E

Front

How do you interpret the rate of change in a real-world context?

Back

The rate of change can represent various real-world scenarios, such as speed, growth rate, or any situation where one quantity changes in relation to another.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the formula for calculating the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5