Understanding Proportional Relationships and Graphs

The video covers graphs of proportional relationships, focusing on writing equations, graphing, and scaling. It includes a card sorting activity to identify proportional relationships and concludes with a homework explanation and summary.

What is the constant of proportionality if a graph has points (8, 14) and (16, 28)?

• 4

• 1/2

• 2

• 7/4

How do you determine the equation of a line from a graph with a constant proportionality of 3?

• y = x/3

• y = 3/x

• y = x + 3

• y = 3x

If a graph has a y/x ratio of 1/4, what is the equation of the line?

• y = 4x

• y = 1/4x

• y = x/4

• y = 4/x

What happens to the appearance of a graph when the scale is changed?

• The graph becomes non-linear

• The slope changes

• The graph's appearance changes but the proportionality remains the same

• The graph disappears

In the water tank example, what is the rate at which Tank B fills?

• 2 liters per minute

• 1.5 liters per minute

• 1 liter per minute

• 0.5 liters per minute

At approximately what time do both tanks have the same amount of water?

• 30 minutes

• 50 minutes

• 80 minutes

• 65 minutes

What is the equation for the relationship between the distance the tortoise runs and the distance the hare runs?

• y = 4/x

• y = x + 4

• y = x/4

• y = 4x

How do you find the constant of proportionality from a table of values?

• Subtract x from y

• Add x and y

• Multiply x by y

• Divide y by x

What transformation is used to show that two figures are similar?

• Reflection

• Translation

• Dilation

• Rotation

According to the lesson, are congruent figures also considered similar?

• No, because they have different angles

• No, because they are not the same size

• Yes, because they have the same shape

• Yes, because a rigid transformation can map one onto the other