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 from 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 on a graph?

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 on a graph?

Back

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

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it involves division by zero (change in x is 0).

Front

How can you identify the slope from a graph visually?

Back

You can identify 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.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the term 'rise' refer to in the context of slope?

Back

'Rise' refers to the vertical change between two points on a line.

Front

What does the term 'run' refer to in the context of slope?

Back

'Run' refers to the horizontal change between two points on a line.