Slopes, parallel, and perpendicular lines

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented by the letter 'm'. It is calculated as the change in y (rise) divided by the change in x (run).

Front

What does a positive slope indicate?

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?

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 formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula is m = (y2 - y1) / (x2 - x1).

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet and have the same slope.

Front

What are perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees) and have slopes that are negative reciprocals of each other.

Front

If the slope of one line is 2, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to it would be -1/2.

Front

What does the 'b' represent in the slope-intercept form of a line (y = mx + b)?

Back

The 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What is the y-intercept of the line y = 3x + 5?

Back

The y-intercept is 5.

Front

How do you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if their slopes are equal.