Finding 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 'm' in the equation of a line (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

Front

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

Back

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

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning there is no change in x as y changes.

Front

Find the slope of the line passing through the points (1, 2) and (3, 6).

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

Find the slope of the line passing through the points (-2, 3) and (4, -5).

Back

The slope is m = (-5 - 3) / (4 - (-2)) = -8 / 6 = -4/3.

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.

Front

What is the slope of a line that is perfectly horizontal?

Back

The slope of a perfectly horizontal line is 0.

Front

If a line has a slope of -5/4, what does this indicate about the direction of the line?

Back

A slope of -5/4 indicates that the line descends from left to right.

Front

If the slope of a line is positive, what can be said about the direction of the line?

Back

If the slope is positive, the line ascends from left to right.