Exploring Systems of Linear Equations

Professor Von Schmohawk introduces the concept of graphing linear equations and their intersections through a race between a tortoise and a hare. The video explains how to graph the distance of each animal over time, derive equations for their paths, and find the intersection point where they meet. The importance of intersection points as common solutions to both equations is highlighted, and the video sets the stage for learning the substitution method in the next lecture.

What does the intersection point of two graphs represent?

• The point where one graph overtakes another

• A common solution to both equations represented by the graphs

• The maximum value of both equations

• The starting point of both equations

At what speed did the tortoise start the race?

• 1.5 miles per hour

• 0.5 miles per hour

• 2 miles per hour

• 1 mile per hour

How long did the hare wait before starting the race?

• 3 hours

• 5 hours

• 2 hours

• 4 hours

What was the hare's speed when he started moving?

• 1.5 miles per hour

• 2 miles per hour

• 0.5 miles per hour

• 1 mile per hour

What is the equation representing the tortoise's distance over time?

• y = x/2

• y = 2x

• y = x - 4

• y = 2x - 8

What is the slope of the hare's graph?

• 2

• 0.5

• 1

• -2

Which point does the hare's equation pass through?

• (0, 4)

• (0, 2)

• (4, 0)

• (2, 0)

What is the equation representing the hare's distance over time?

• y = x/2

• y = 2x

• y = x - 4

• y = 2x - 8

Why are only the positive coordinates of the lines meaningful in this context?

• Because the race track is circular

• Because time and distance cannot be negative in this scenario

• Because the equations only work with positive numbers

• Because negative coordinates represent a different race

What mathematical technique will be introduced to find the intersection point?

• Differentiation

• Substitution

• Graphing

• Integration