11/19 Linear Functions

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value).

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

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

Front

How can you identify a function from a mapping diagram?

Back

In a mapping diagram, a function is identified if each input (x-value) is connected to only one output (y-value).

Front

What is the significance of a negative slope in a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

What is the formula to find the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does it mean if a linear function has a slope of zero?

Back

A slope of zero means the line is horizontal, indicating that the y-value remains constant regardless of the x-value.

Front

How do you convert the equation of a line from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.