Understanding Horizontal and Vertical Lines

The video tutorial explains how to write the equation of a horizontal line passing through a given point. It begins by plotting the point on a coordinate plane and analyzing the horizontal line through it. The tutorial demonstrates that the equation of a horizontal line is y equals the y-coordinate of the point. It also generalizes this concept, stating that any horizontal line through a point (a, b) has the equation y = b, and any vertical line through the same point has the equation x = a. The video concludes with a brief summary and helpful remarks.

What is the first step in finding the equation of a horizontal line through a specific point?

• Plot the point on the coordinate plane

• Calculate the slope of the line

• Determine the y-intercept of the line

• Identify the x-coordinate of the point

Where would the point (7, -2) be located on the coordinate plane?

• In the fourth quadrant

• In the first quadrant

• In the second quadrant

• In the third quadrant

What is the equation of a horizontal line passing through the point (7, -2)?

• x = 7

• y = 7

• y = -2

• x = -2

How can you generalize the equation of any horizontal line passing through a point (a, b)?

• y = b

• x = a

• y = a

• x = b

Why does every point on a horizontal line have the same y-coordinate?

• Because the line passes through the origin

• Because the line is parallel to the y-axis

• Because the line has a positive slope

• Because the line is parallel to the x-axis

What is the equation of a vertical line passing through the point (a, b)?

• x = a

• y = a

• x = b

• y = b

What characteristic do all points on a vertical line share?

• They have the same y-coordinate

• They have the same x-coordinate

• They all pass through the origin

• They are all in the same quadrant