SLOPE

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 to the horizontal change between two points on the line.

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 the x-value increases, the y-value 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 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 regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

If a line has a slope of 2, what does this mean in terms of rise over run?

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

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the vertical change (rise) and the horizontal change (run), and then use the formula: slope = rise/run.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

The slope is (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, growth, or decline, and is used in various fields like physics, economics, and engineering.