Slope

Front

What is the definition of slope?

Back

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

Front

What is the formula for calculating slope?

Back

The formula for slope (m) is given by: m = \frac{y_2 - y_1}{x_2 - x_1}, where (x_1, y_1) and (x_2, y_2) are two points on the line.

Front

How do you find the slope of a line from a graph?

Back

To find the slope from a graph, count the vertical change (rise) and the horizontal change (run) between two points on the line. Use the formula: Slope = Rise/Run.

Front

What does a positive slope indicate?

Back

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

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, 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, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run is 0 and division by zero is not possible.

Front

If a line has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit of horizontal change (run), there is a 2 unit increase in vertical change (rise).

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope of the line y = 3x + 1 is 3, which is the coefficient of x.

Front

How do you interpret a slope of \frac{1}{2}?

Back

A slope of \frac{1}{2} means that for every 2 units of horizontal change (run), there is a 1 unit increase in vertical change (rise).