Perpendicular and Parallel Lines

Front

What is the definition of parallel lines?

Back

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

Front

What is the definition of perpendicular lines?

Back

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

Front

How do you find the slope of a line given its equation in the form y = mx + b?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the slope of the line represented by the equation y = 2x + 4?

Back

The slope is 2.

Front

If two lines have slopes m1 and m2, under what condition are they perpendicular?

Back

They are perpendicular if m1 * m2 = -1.

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

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

Back

Two lines are parallel if they have the same slope.

Front

What is the slope of the line given by the equation 3y = 6x + 9?

Back

First, rewrite in slope-intercept form: y = 2x + 3. The slope is 2.

Front

Write the equation of a line parallel to y = 3x + 1 that passes through the point (2, 5).

Back

The equation is y = 3x - 1.

Front

What is the y-intercept of the line represented by the equation y = -x + 4?

Back

The y-intercept is (0, 4).