Alg Linear Functions 11/06/24

Front

What is the definition of the average rate of change of a function over an interval?

Back

The average rate of change of a function over an interval [a, b] is defined as the change in the function's value divided by the change in the input value, calculated as (f(b) - f(a)) / (b - a).

Front

How do you determine the slope of a linear function from its equation?

Back

The slope of a linear function in the form y = mx + b is represented by the coefficient m, which indicates the steepness and direction of the line.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the function is increasing.

Front

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

Back

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

Front

How can you interpret the slope in a real-world context?

Back

The slope can represent the rate of change in a real-world scenario, such as speed, cost per unit, or growth rate.

Front

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

Back

A slope of zero indicates that the function is constant; there is no change in the y-value as the x-value changes.

Front

How do you find the slope of a line given two points on the line?

Back

To find the slope, use the formula m = (y2 - y1) / (x2 - x1) by substituting the coordinates of the two points.

Front

What is the relationship between the slopes of parallel and perpendicular lines?

Back

Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.

Front

How can you determine if a function is linear from its graph?

Back

A function is linear if its graph forms a straight line, indicating a constant rate of change.