Slope and Rate of Change

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a line?

Back

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

Front

How do you find the slope from an equation in slope-intercept form?

Back

In the slope-intercept form of a line (y = mx + b), the slope 'm' is the coefficient of x.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where x remains constant while y changes, indicating a division by zero in the slope formula.

Front

How do you calculate 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 slope of the line represented by the equation y = 3/2x + 3?

Back

The slope is 3/2.

Front

What is the y-intercept of the line represented by the equation y = 3/2x + 3?

Back

The y-intercept is (0, 3).