Understanding Tangent Line Slopes

The video tutorial explains how to estimate the slope of tangent lines at various points on a graph. It begins with calculating the slope at x = -3 using both graphical and formulaic methods, resulting in a slope of approximately 2.7. The tutorial then moves to x = 0, where the slope is found to be approximately -2. Finally, at x = 1.8, the tangent line is horizontal, indicating a slope of zero. The video emphasizes understanding the change in y over the change in x and provides a step-by-step approach to using the slope formula.

What is the approximate y-coordinate of the point of tangency when x = -3?

• 2.5

• 4.0

• 3.0

• 3.7

Which of the following points is used to calculate the slope at x = -3?

• (-4, 1)

• (-2, 2)

• (-3, 3.7)

• (0, 3)

How is the slope of a line generally calculated?

• Change in y divided by change in x

• Difference of x and y

• Change in x divided by change in y

• Sum of x and y

What is the slope of the tangent line at x = 0?

• -2

• 3

• 0

• 2

Which point is used along with (0, 3) to find the slope at x = 0?

• (0, 2)

• (1, 4)

• (1, 3)

• (-1, 5)

What is the y-coordinate of the point of tangency at x = 1.8?

• 0.5

• 1.0

• 1.5

• 2.0

What is the slope of the tangent line at x = 1.8?

• 1

• 0

• -1

• 2

Which of the following points is used to determine the slope at x = 1.8?

• (1, 0)

• (3, 1)

• (4, 0.5)

• (2, 0.5)

What does a horizontal tangent line indicate about the slope?

• Slope is undefined

• Slope is positive

• Slope is negative

• Slope is zero

What is the main takeaway from the video regarding tangent lines?

• Tangent lines always have a positive slope

• Tangent lines can have varying slopes

• Tangent lines are always horizontal

• Tangent lines are not useful