3.3 Slopes of Lines

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

What does a positive slope indicate about a line?

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 about a line?

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 is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero because there is no change in y as x changes.

Front

How do you find 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 is the relationship between the slopes of two perpendicular lines?

Back

The slopes of two perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.

Front

If two lines have the same slope, what can be said about them?

Back

If two lines have the same slope, they are parallel and will never intersect.

Front

What is the slope of a line that is perpendicular to a line with a slope of 1/4?

Back

The slope of the perpendicular line is -4.

Front

What is the slope of a line that is parallel to a line with a slope of -1/3?

Back

The slope of the parallel line is also -1/3.