Finding the 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 (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope from 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 on a graph?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

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, meaning the line falls from left to right.

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 would require division by zero (no horizontal change).

Front

If a line has a slope of 4/1, what does this mean in terms of rise and run?

Back

A slope of 4/1 means that for every 1 unit of horizontal change (run), there is a 4 unit increase in vertical change (rise).

Front

How can you identify the slope of a line from its graph?

Back

To identify the slope from a graph, select two points on the line, determine the rise and run between them, and calculate the slope using the formula m = rise/run.

Front

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

Back

The slope of a perfectly vertical line is undefined.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal and there is no change in the y-value as the x-value changes.