4.5 Parallel Lines

Front

What is the definition of parallel lines?

Back

Parallel lines are lines in a plane that never meet; they are always the same distance apart and have the same slope.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of a line parallel to a line with slope 2/3?

Back

The slope of a line parallel to a line with slope 2/3 is also 2/3.

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do 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 represented by the equation 4x + 3y = -3?

Back

To find the slope, rewrite in slope-intercept form: y = -rac{4}{3}x - 1, so the slope is -rac{4}{3}.

Front

Which of the following equations represents a line parallel to y = rac{4}{3}x - 2?

Back

Any line of the form y = rac{4}{3}x + b, where b is any real number, is parallel.

Front

If a line has a slope of -2, what is the slope of a line parallel to it?

Back

The slope of a line parallel to it is also -2.

Front

What is the relationship between the slopes of two parallel lines?

Back

The slopes of two parallel lines are equal.

Front

How can you identify parallel lines from a set of equations?

Back

Compare the slopes of the equations; if they are equal, the lines are parallel.