Slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How is slope calculated?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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 does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where the change in x is zero, leading to division by zero in the slope formula.

Front

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

Back

A slope of 2 means that for every 1 unit increase in x, the y-value increases by 2 units.

Front

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

Back

The slope of the line is 3, which means it rises 3 units for every 1 unit it moves to the right.

Front

What is the slope of the line represented by the equation y = -1/4x + 2?

Back

The slope of the line is -1/4, indicating that for every 4 units moved to the right, the line falls 1 unit.

Front

How do you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and calculate the slope using m = rise/run.