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 an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down and does not have a defined angle.

Front

What does a positive slope indicate about the direction of a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about the direction of a line?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, resulting in a downward slant from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as the x-coordinate changes.

Front

How can you determine the slope from the equation of a line in slope-intercept form (y = mx + b)?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

What is the slope of the line represented by the equation y = -2x + 5?

Back

The slope of the line is -2.

Front

If a line passes through the points (10, 1) and (5, 2), what is the slope?

Back

The slope of the line is -1/5.

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, in various real-world contexts.