Parallel and Perpendicular Lines

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet. They have the same slope but different y-intercepts.

Front

What are perpendicular lines?

Back

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

Front

What does 'm' represent in the equation y=mx+b?

Back

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

Front

What does 'b' represent in the equation y=mx+b?

Back

In the equation y=mx+b, 'b' represents the y-intercept of the line.

Front

How do you determine if two lines are parallel from their equations?

Back

Two lines are parallel if they have the same slope. For example, the lines y=-rac{1}{4}x-1 and y=-rac{1}{4}x+5 are parallel.

Front

How do you determine if two lines are perpendicular from their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1. For example, if one line has a slope of 2, the other must have a slope of -rac{1}{2}.

Front

Write the equation of a line parallel to y=3x+2 that passes through the point (1, 4).

Back

The equation is y=3x-1.

Front

Write the equation of a line perpendicular to y=2x+3 that passes through the point (2, 5).

Back

The equation is y=-rac{1}{2}x+6.

Front

What is the slope of the line represented by the equation y=5?

Back

The slope is 0, indicating a horizontal line.

Front

What is the slope of the line represented by the equation x=4?

Back

The slope is undefined, indicating a vertical line.