Slopey Slope

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, defined as the ratio of the rise (change in y) to the run (change in x).

Front

How is slope calculated between 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?

Back

A positive slope indicates that as x increases, y also increases, 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 x increases, y 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 rise over the run.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run is 0.

Front

Find the slope of the line that passes through the points (2, 3) and (4, 7).

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).

Front

Find the slope of the line that passes through the points (1, 1) and (3, 5).

Back

The slope is 2, calculated as (5 - 1) / (3 - 1).

Front

If a line has a slope of -3, what does this tell you about the line's direction?

Back

The line falls steeply from left to right, indicating a negative relationship between x and y.

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope is 4, which is the coefficient of x in the equation.