Understanding Lines and Rectangles

The video tutorial covers writing equations for vertical and horizontal lines, plotting points with constant x or y coordinates, and understanding the relationship between x and y values in graphing. It also explores drawing rectangles on a graph, writing equations for their sides, and examining rectangles with a fixed perimeter. The lesson concludes with a summary and homework instructions.

Which of the following sets of lines are not parallel?

• Lines that are equidistant from each other

• Lines that intersect at one point

• Lines that never intersect

• Lines with the same slope

What is the equation of a line where all points have a y-coordinate of -4?

• x = -4

• y = 4

• y = -4

• x = 4

If a line is vertical, what can be said about its equation?

• It has a negative slope

• It has a positive slope

• It has a constant x-value

• It has a constant y-value

Which equation represents a horizontal line?

• x = 5

• y = 5

• x = -5

• y = -5

What is the equation of a line that passes through the points (2, 1) and (2, 3)?

• y = 2

• y = 1

• x = 3

• x = 2

How do you determine the equation of a line that forms one side of a rectangle with vertices at (2, 1), (5, 1), (5, 3), and (2, 3)?

• Identify the constant x or y value

• Calculate the distance between vertices

• Find the midpoint of the vertices

• Use the slope of the line

If a rectangle has a perimeter of 50 units, what must the sum of its length and width be?

• 50

• 25

• 100

• 75

What happens to the width of a rectangle if its length decreases by one unit, given a fixed perimeter?

• The width decreases by one unit

• The width increases by one unit

• The width remains the same

• The width doubles

What is the slope of a line that decreases by one unit in y for every one unit increase in x?

• 1

• -1

• 0

• Undefined

If a book's cover has a thickness of 1/4 inch and the pages add 1/4 inch per 100 pages, what is the equation for the book's thickness?

• y = 1/2x + 1/2

• y = 1/4x + 1/4

• y = 1/4x + 1/2

• y = 1/2x + 1/4