The video tutorial explains how to graph absolute value functions and linear equations to find points of intersection. It begins with an introduction to graphing techniques, followed by a visual approach to graphing y = |x - 1|. The tutorial covers reflecting graphs across the x-axis and emphasizes the importance of labeling. It then demonstrates graphing y = 0.5x + 1, comparing slopes, and concludes with identifying intersection points to solve equations.

What is the primary technique used to solve the original equation in the video?

• Graphing the functions

• Using algebraic manipulation

• Substituting values

• Using a calculator

What does the graph of y = |x - 1| look like?

• A circle

• A straight line

• A parabola

• A V-shaped graph

How does the graph of y = x - 1 relate to y = |x - 1|?

• They are identical

• y = |x - 1| is a reflection of y = x - 1

• y = |x - 1| is a translation of y = x - 1

• y = |x - 1| is a rotation of y = x - 1

What happens to the graph of y = x - 1 when absolute value is applied?

• It remains unchanged

• It becomes a horizontal line

• It reflects over the y-axis

• It reflects over the x-axis

What is the result of reflecting the negative part of y = x - 1?

• It becomes y = x + 1

• It becomes y = 1 - x

• It becomes a vertical line

• It becomes a horizontal line

What is the y-intercept of the graph y = 0.5x + 1?

• -1

• 0

• 2

• 1

How does the slope of y = 0.5x + 1 compare to y = x - 1?

• It is inverted

• It is less steep

• It is the same

• It is steeper

What is the purpose of graphing both functions on the same set of axes?

• To determine their y-intercepts

• To see which is steeper

• To find points of intersection

• To compare their slopes

Why is the branch y = 0.5x - 1 irrelevant in finding intersections?

• It is a vertical line

• It does not intersect with the other graph

• It is parallel to the x-axis

• It is outside the graph range

What is the significance of labeling the branches of the graph?

• To identify the color of the graph

• To determine the length of the graph

• To calculate the area under the graph

• To easily identify points of intersection