Slope From a Graph

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

How is slope calculated using two points (x1, y1) and (x2, y2)?

Back

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 the x-values increase, the y-values also increase, resulting in an upward trend.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, resulting in a downward trend.

Front

What is an undefined slope, and when does it occur?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change (x2 - x1 = 0), making the slope calculation impossible.

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 the x-values change.

Front

How can you determine the slope from a graph visually?

Back

To determine the slope from a graph, select two points on the line, count the vertical change (rise) and the horizontal change (run), and calculate the slope as rise/run.

Front

What is the slope of a line that rises 3 units for every 4 units it runs?

Back

The slope of the line is 3/4.

Front

If a line has a slope of -2, what does this tell you about its direction?

Back

A slope of -2 indicates that the line descends steeply; for every 2 units it falls vertically, it moves 1 unit horizontally to the right.

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.