Slope from a Graph

Front

What is the slope of a line?

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 from a graph?

Back

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

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing a downward trend.

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 because the run (change in x) is 0, leading to division by zero.

Front

If a line rises 3 units for every 4 units it runs, what is the slope?

Back

The slope is 3/4.

Front

If a line falls 2 units for every 5 units it runs, what is the slope?

Back

The slope is -2/5.

Front

What is the slope of a line that goes through the points (1, 2) and (3, 6)?

Back

The slope is (6-2)/(3-1) = 4/2 = 2.

Front

What does it mean if the slope is undefined?

Back

An undefined slope means the line is vertical, indicating that there is no horizontal change.