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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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.

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What does it mean for a linear function to have a positive slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does it mean for a linear function to have a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

How do you write an equation from a word problem involving linear functions?

Back

Identify the variables, determine the relationship between them, and express it in the form of a linear equation.

Front

What is the significance of the point (0, b) in a linear function?

Back

The point (0, b) is the y-intercept, indicating the value of y when x is zero.