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 is a positive slope characterized?

Back

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

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no vertical change as the x-value changes.

Front

What does an undefined slope represent?

Back

An undefined slope occurs in vertical lines, where the x-value remains constant while the y-value changes, resulting in a division by zero in the slope formula.

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 is the slope of a line that goes from the point (2, 3) to (5, 7)?

Back

The slope is calculated as m = (7 - 3) / (5 - 2) = 4 / 3.

Front

What type of slope does a line that is perfectly horizontal have?

Back

A perfectly horizontal line has a slope of zero.

Front

What type of slope does a line that is perfectly vertical have?

Back

A perfectly vertical line has an undefined slope.

Front

If a line has a slope of -2, what does this indicate about the line's direction?

Back

A slope of -2 indicates that for every 1 unit increase in the x-direction, the y-value decreases by 2 units, resulting in a downward slope.