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

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, resulting in an upward trend 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, resulting in a downward trend from left to right.

Front

What does an undefined slope indicate?

Back

An undefined slope occurs in vertical lines where the change in x is zero, meaning there is no horizontal movement.

Front

How is the slope of a line calculated using two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-values change.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3, which indicates that for every unit increase in x, y increases by 3 units.

Front

If a line has a slope of -1, what does this imply about the relationship between x and y?

Back

A slope of -1 implies that for every unit increase in x, y decreases by 1 unit, indicating a negative linear relationship.

Front

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

Back

The slope of the line x = 4 is undefined, as it is a vertical line.

Front

How can you determine the slope from a graph?

Back

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