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 (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be 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-values increase, the y-values also increase, 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-values increase, the y-values decrease, 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 zero, 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 zero, leading to division by zero in the slope formula.

Front

How can you determine which line is the steepest among multiple lines?

Back

The steepness of a line can be determined by comparing the absolute values of their slopes; the line with the largest absolute value of slope is the steepest.

Front

If a line has a slope of 5/2, what does this mean in terms of rise and run?

Back

A slope of 5/2 means that for every 2 units of horizontal change (run), the line rises 5 units (rise).

Front

What is the slope of the line that passes through the points (10, 1) and (5, 2)?

Back

The slope of the line that passes through (10, 1) and (5, 2) is -1/5.

Front

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

Back

A zero slope indicates a constant value, meaning there is no change in the dependent variable regardless of changes in the independent variable.