How to solve a system of equations of two perpendicular lines by graphing

The video tutorial covers the identification and graphing of perpendicular lines in a system of equations. It begins by discussing the concepts of parallel and perpendicular lines, assuming prior knowledge. The instructor explains how to identify perpendicular lines by examining slopes, noting that they are reciprocals and have opposite signs. The tutorial then demonstrates graphing these lines to verify that they intersect at a single point, confirming a consistent and independent solution.

What is a key characteristic of perpendicular lines in terms of their slopes?

• Their slopes are both negative.

• They have the same slope.

• Their slopes are both positive.

• Their slopes are reciprocals and have opposite signs.

What happens when two lines have slopes that are reciprocals of each other?

• The lines do not intersect.

• The lines overlap completely.

• The lines are perpendicular.

• The lines are parallel.

What is the significance of a 90-degree angle in the context of line intersections?

• It indicates no intersection.

• It indicates overlapping lines.

• It indicates perpendicular lines.

• It indicates parallel lines.

What does it mean if two lines have the same y-intercept?

• They are parallel.

• They are perpendicular.

• They do not intersect.

• They intersect at the y-intercept.

How can you determine if a system of equations is consistent and independent?

• The lines overlap completely.

• The lines do not intersect.

• The lines intersect at exactly one point.

• The lines are parallel.