Finding 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, indicating that there is no vertical change as you move along the line.

Front

What is the slope of a vertical line?

Back

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

Front

If a line rises 3 units for every 2 units it runs, what is the slope?

Back

The slope is 3/2.

Front

If a line falls 2 units for every 3 units it runs, what is the slope?

Back

The slope is -2/3.

Front

What does it mean if a line has a slope of 1/3?

Back

It means that for every 1 unit the line rises, it runs 3 units to the right.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the slope formula m = rise/run.