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?

Back

Two lines are parallel if they have the same slope. For example, the lines represented by the equations y = 2x + 3 and y = 2x - 5 are parallel.

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

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

Back

The equation is y = 2x - 5.

Front

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

Back

The equation is y = 3x + 2.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x = 0.

Front

Write an equation for the line parallel to y = -3x + 4 that passes through (1, 5).

Back

The equation is y = -3x + 8.

Front

How do you convert the standard form of a line to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = - (A/B)x + (C/B).

Front

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

Back

The equation is y = -\frac{5}{2}x - 8.

Front

What is the relationship between the slopes of parallel lines?

Back

The slopes of parallel lines are equal.