Slope from a Graph

Front

What is the definition of slope in mathematics?

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 is slope calculated from two points (x1, y1) and (x2, y2)?

Back

Slope (m) is calculated using the formula: 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 an undefined slope represent?

Back

An undefined slope represents a vertical line, where the change in x is zero, leading to division by zero in the slope formula.

Front

What does a zero slope represent?

Back

A zero slope represents a horizontal line, where there is no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero.

Front

If a line has a slope of -5/3, what does this indicate about its direction?

Back

A slope of -5/3 indicates that for every 3 units moved to the right (positive x-direction), the line moves down 5 units (negative y-direction).

Front

How can you determine the type of slope from a graph?

Back

You can determine the type of slope by observing the direction of the line: rising (positive), falling (negative), horizontal (zero), or vertical (undefined).