Parallel and Perpendicular Equations

Front

What is the definition of parallel lines in the context of linear equations?

Back

Parallel lines are lines in a plane that do not intersect and have the same slope.

Front

What is the definition of perpendicular lines in the context of linear equations?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees) and have slopes that are negative reciprocals of each other.

Front

How do you find the slope of a line given its equation in slope-intercept form?

Back

The slope of a line in slope-intercept form (y = mx + b) is the coefficient 'm' of 'x'.

Front

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

Back

The slope of a line that is parallel to it will also be 3.

Front

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

Back

The slope of a line that is perpendicular to it will be 1/2 (the negative reciprocal of -2).

Front

What is the slope of the line represented by the equation y = 5x + 2?

Back

The slope of the line is 5.

Front

How do you write the equation of a line that is parallel to a given line and passes through a specific point?

Back

Use the same slope as the given line and apply the point-slope form of the equation: y - y1 = m(x - x1).

Front

What is the slope of a line that is parallel to the line y = -4x + 7?

Back

The slope of a line that is parallel to it is -4.

Front

What is the slope of a line that is perpendicular to the line y = 1/2x - 3?

Back

The slope of a line that is perpendicular to it is -2 (the negative reciprocal of 1/2).

Front

How do you determine the y-intercept of a line given its slope and a point on the line?

Back

Use the slope-intercept form y = mx + b and substitute the slope and the coordinates of the point to solve for b.