Types of Slope

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 to the horizontal change between two points on the line.

Front

What is the formula for calculating the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The formula for slope is m = (y2 - y1) / (x2 - x1).

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down, and there is no horizontal change.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating there is no vertical change as you move along the line.

Front

How do you determine if a slope is positive or negative?

Back

A slope is positive if it rises from left to right and negative if it falls from left to right.

Front

What is the slope of a line that decreases as you move from left to right?

Back

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

Front

If a line has a slope of -3/2, what does this indicate about its steepness?

Back

A slope of -3/2 indicates that for every 2 units you move horizontally to the right, the line moves down 3 units, making it relatively steep.

Front

What is the relationship between slope and the angle of inclination of a line?

Back

The slope of a line is equal to the tangent of the angle of inclination (θ) with respect to the horizontal axis, expressed as m = tan(θ).

Front

What does a slope of 4/0 represent?

Back

A slope of 4/0 is undefined, indicating a vertical line since there is no horizontal change.

Front

How can you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, determine the vertical and horizontal distances between them, and use the slope formula (rise/run).