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 (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

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, 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 the x-values increase, the y-values decrease, 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 vertical change as the x-values change.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the x-values are constant, indicating that there is no horizontal change.

Front

If a line has a slope of -5/3, what does this tell you about its steepness and direction?

Back

A slope of -5/3 indicates that the line is steep and falls from left to right, with a vertical change of 5 units for every 3 units of horizontal change.

Front

What type of slope does a horizontal line have?

Back

A horizontal line has a slope of zero.

Front

What type of slope does a vertical line have?

Back

A vertical line has an undefined slope.

Front

If a line has a slope of 1, what does this indicate about the relationship between x and y?

Back

A slope of 1 indicates that for every 1 unit increase in x, there is a corresponding 1 unit increase in y, meaning the line rises at a 45-degree angle.