Understanding Slopes and Their Effects

The video tutorial covers lesson nine, focusing on the concept that slopes can be positive, negative, or zero. It explains how to reflect lines and use slope triangles to derive equations. The lesson includes examples of positive and negative slopes, as well as a scenario with a zero slope, illustrating how changes in x and y values affect the slope. The tutorial emphasizes understanding the relationship between slope and rate of change.

What is the main idea introduced in the beginning of the lesson?

• Slopes can be negative or zero.

• Slopes are always positive.

• Slopes are only used in physics.

• Slopes are irrelevant in geometry.

In the snow melting scenario, what is the rate of change of the snow depth?

• 10 inches per hour

• 2 inches per hour

• 1 inch per hour

• 5 inches per hour

What is the equation of the line when the slope is positive 1?

• y = 1x + 25

• y = 1x + 20

• y = 1x + 30

• y = 1x + 15

How does a negative slope affect the direction of a line?

• It forms a vertical line.

• It remains horizontal.

• It goes from upper left to lower right.

• It goes from lower left to upper right.

What does a zero slope indicate about the change over time?

• The quantity is increasing.

• The quantity fluctuates.

• The quantity is decreasing.

• There is no change in the quantity.

In the fare card example, what is the slope of the line representing the balance over time?

• Positive

• Negative

• Undefined

• Zero

What happens to the fare card balance if the slope is positive?

• The balance decreases.

• The balance remains constant.

• The balance becomes zero.

• The balance increases.

How is a negative slope represented in the context of the fare card?

• The balance doubles.

• The balance decreases over time.

• The balance remains unchanged.

• The balance increases over time.

What is the effect of a zero slope on the fare card balance after several days?

• The balance increases.

• The balance becomes negative.

• The balance remains the same.

• The balance decreases.

If the fare is doubled, what happens to the slope of the line representing the fare card balance?

• The slope becomes undefined.

• The slope becomes more negative.

• The slope becomes positive.

• The slope remains zero.