381 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

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

Back

Two lines are parallel if their slopes are equal. For example, in the equations y = mx + b, if both lines have the same 'm', they are parallel.

Front

How do you find the slope of a line from its equation in standard form?

Back

To find the slope from the standard form Ax + By = C, rearrange to slope-intercept form (y = mx + b) to identify 'm'.

Front

What is the slope of the line 5x + 2y = 8?

Back

Rearranging to slope-intercept form gives y = -5/2x + 4, so the slope is -5/2.

Front

What is the negative reciprocal of 2?

Back

The negative reciprocal of 2 is -1/2.

Front

If a line has a slope of 4, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to a line with a slope of 4 is -1/4.

Front

What is the equation of a line parallel to y = 3x + 2?

Back

Any line parallel to y = 3x + 2 will have the form y = 3x + b, where b is any real number.

Front

How do you find the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the x-intercept of the line y = 4x + 8?

Back

Set y = 0: 0 = 4x + 8, so x = -2. The x-intercept is -2.