Slope and Rate of Change

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

How is slope calculated?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, meaning there is no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

If a line has a slope of -5/3, what does this mean?

Back

A slope of -5/3 means that for every 3 units you move to the right (positive x-direction), you move down 5 units (negative y-direction).

Front

What is the slope of a line that goes up from left to right?

Back

The slope of a line that goes up from left to right is positive.

Front

What is the slope of a line that goes down from left to right?

Back

The slope of a line that goes down from left to right is negative.

Front

What does it mean if a slope is zero?

Back

A slope of zero means the line is horizontal and there is no change in the y-value as the x-value changes.