Slope from a Graph

Front

What is the definition of slope in a graph?

Back

The slope of a line is a measure of its steepness, 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 of a line given 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 slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning there is no horizontal change as you move along the line.

Front

If a line has a positive slope, what does this tell you about the direction of the line?

Back

A positive slope indicates that the line rises from left to right.

Front

If a line has a negative slope, what does this tell you about the direction of the line?

Back

A negative slope indicates that the line falls from left to right.

Front

What is the slope of a line that passes through the points (2, 3) and (4, 7)?

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What is the slope of a line that passes through the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

What is the slope of a line that passes through the points (3, 4) and (5, 4)?

Back

The slope is 0 because the y-coordinates are the same, indicating a horizontal line.

Front

How can you determine the slope from a graph visually?

Back

You can determine the slope by selecting two points on the line, measuring the vertical rise and horizontal run between them, and calculating the ratio of rise to run.