Slope of a Line

Front

What is the slope of a line?

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 positive slope indicate about a line?

Back

A positive slope indicates that as you move from left to right along the line, the line rises. This means that the y-value increases as the x-value increases.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as you move from left to right along the line, the line falls. This means that the y-value decreases as the x-value increases.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change (run) is 0, leading to division by zero in the slope formula.

Front

If a line rises 4 units and runs 2 units, what is the slope?

Back

The slope is 4/2 = 2.

Front

If a line falls 3 units and runs 6 units, what is the slope?

Back

The slope is -3/6 = -1/2.

Front

What does the slope of 2/3 mean in terms of rise and run?

Back

A slope of 2/3 means that for every 3 units you move to the right (run), the line rises 2 units (rise).

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 rise (vertical change) and run (horizontal change) between them, and use the slope formula m = rise/run.