Exploring Linear Equations Fundamentals

The video tutorial covers creating tables, graphs, and equations to model proportional relationships. It begins with a word problem about a person walking two miles in 30 minutes and explores how far they can walk over several hours. The teacher explains the calculation of distance over time, models the relationship on a graph, and derives the equation y = 4x to represent the relationship. The lesson concludes with a summary of the concepts covered.

What are we going to work on today?

• Studying historical events

• Solving quadratic equations

• Creating tables, graphs, and writing equations to model proportional relationships

• Learning about geometric shapes

If a person can walk 2 miles in 30 minutes, how far can they walk in 1 hour?

• 8 miles

• 6 miles

• 4 miles

• 2 miles

How many miles can a person walk in 20 hours at the same pace?

• 100 miles

• 40 miles

• 60 miles

• 80 miles

What is the expression to calculate the distance walked after x hours?

• 2x

• 3x

• 4x

• 5x

On the graph, what does the x-axis represent?

• Miles traveled

• Hours

• Speed

• Distance

On the graph, what does the y-axis represent?

• Distance

• Speed

• Hours

• Miles traveled

What is the coordinate for 1 hour on the graph?

• (1, 8)

• (1, 6)

• (1, 4)

• (1, 2)

What is the coordinate for 2 hours on the graph?

• (2, 8)

• (2, 4)

• (2, 6)

• (2, 10)

What is the equation that represents the proportional relationship?

• y = 2x

• y = 3x

• y = 4x

• y = 5x

If you replace x with 5 in the equation y = 4x, what is the value of y?

• 25

• 10

• 15

• 20