4.5 Parallel Lines

Front

What are 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 determine if two lines are parallel using their equations?

Back

Two lines are parallel if they have the same slope. For lines in the form y = mx + b, the value of m (the coefficient of x) must be the same.

Front

What is the slope-intercept form of a line?

Back

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

Front

Convert the equation -3x + 3y = 12 to slope-intercept form.

Back

The slope-intercept form is y = x + 4.

Front

Which equation is parallel to y = 2x + 3?

Back

Any equation of the form y = 2x + b, where b is any real number, is parallel to y = 2x + 3.

Front

What is the slope of the line represented by the equation 5x + 6y = 12?

Back

The slope is -rac{5}{6}.

Front

If two lines have slopes m_1 and m_2, what condition must be satisfied for them to be parallel?

Back

m_1 must equal m_2.

Front

Identify the slope of the line given by the equation y = -3x + 2.

Back

The slope is -3.

Front

What is the y-intercept of the line y = 4x - 5?

Back

The y-intercept is -5.

Front

Which of the following lines is parallel to y = -rac{1}{2}x + 4?

Back

Any line of the form y = -rac{1}{2}x + b, where b is any real number.