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 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?

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?

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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no vertical change as the x-values change.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where the x-values are constant, leading to a division by zero in the slope formula.

Front

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

Back

A slope of 4 means that for every 1 unit of horizontal change (run), the vertical change (rise) is 4 units.

Front

What is the slope of a line that runs parallel to the x-axis?

Back

The slope of a line parallel to the x-axis is 0.

Front

What is the slope of a line that runs parallel to the y-axis?

Back

The slope of a line parallel to the y-axis is undefined.

Front

How can you determine the slope from a graph visually?

Back

To determine the slope visually, select two points on the line, count the vertical rise and horizontal run between them, and calculate the slope as rise/run.