Slope and Rate of Change

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates that the line is vertical, meaning there is no horizontal change as you move along the line.

Front

If the slope of a line is positive, what does that tell you about the line's direction?

Back

A positive slope indicates that the line rises from left to right.

Front

If the slope of a line is negative, what does that tell you about the line's direction?

Back

A negative slope indicates that the line falls from left to right.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

Front

What is the slope of the line represented by the equation y = -rac{1}{2}x + 4?

Back

The slope of the line is -rac{1}{2}.

Front

Find the slope of the line passing through the points (1, 2) and (3, 6).

Back

The slope is 2.

Front

What is the rate of change in the context of a linear function?

Back

The rate of change is the same as the slope; it represents how much the dependent variable changes for a unit change in the independent variable.