Parallel and Perpendicular Lines

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

What is the slope-intercept form of a linear equation?

Back

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

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 would also be 2.

Front

If a line has a slope of 3, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to it would be -1/3.

Front

What is the y-intercept of the line y = 4x + 3?

Back

The y-intercept is 3, 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

If the coefficients of 'x' in both equations are the same, the lines are parallel.

Front

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

Back

If the slopes of the two lines are negative reciprocals of each other, the lines are perpendicular.

Front

What is the equation of a line with a slope of -1 that passes through the point (2, 3)?

Back

The equation is y - 3 = -1(x - 2), which simplifies to y = -x + 5.