Coordinate Geometry

Front

What is the definition of parallel lines in coordinate geometry?

Back

Parallel lines are lines in a plane that never meet. They have the same slope but different y-intercepts.

Front

How do you determine if two lines are parallel given their equations?

Back

Two lines are parallel if their slopes are equal. For example, in the equations y = mx + b, if both lines have the same value of m, they are parallel.

Front

What is the slope of a line represented by the equation y = mx + b?

Back

The slope of the line is represented by the coefficient m in the equation y = mx + b.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other line's slope will be -1/m.

Front

How can you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

What does it mean for two lines to intersect?

Back

Two lines intersect if they cross each other at a point. This occurs when their slopes are different.

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, represented by the value of b in the equation y = mx + b.

Front

How can you determine if two lines are intersecting or parallel from their equations?

Back

If the slopes of the two lines are equal, they are parallel. If the slopes are different, they intersect.

Front

What is the slope of the line represented by the equation y = 4x + 3?

Back

The slope of the line is 4.