Slope from a Graph

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 is the slope of a horizontal line?

Back

The slope of a horizontal line is zero, 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 there is no horizontal change (run) while there is a vertical change (rise).

Front

How do you calculate slope using the rise/run method?

Back

To calculate slope using the rise/run method, divide the vertical change (rise) by the horizontal change (run) between two points on the line.

Front

If a line rises 5 units and runs 3 units, what is the slope?

Back

The slope is \\frac{5}{3}.

Front

If a line falls 3 units and runs 1 unit, what is the slope?

Back

The slope is -3, indicating a negative slope.

Front

What is the slope of a line that does not change in height as it moves horizontally?

Back

The slope is zero, indicating a horizontal line.

Front

What is the formula for slope given two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = \\frac{y2 - y1}{x2 - x1}.