Understanding Secant Lines and Slopes

The video tutorial explains how to find the slope of a secant line that intersects the curve y = ln(x) at two points with x-coordinates 2 and 2 + h. It begins by identifying the y-coordinates for these x-values using the natural logarithm function. The tutorial then derives the slope of the secant line by calculating the change in y over the change in x. Finally, it provides a visual representation of the secant line on a graph to aid understanding.

What is a secant line in the context of a curve?

• A line that is parallel to the curve

• A line that intersects the curve at two points

• A line that touches the curve at one point

• A line that is perpendicular to the curve

Tags

CCSS.HSF.BF.B.5

If x = 2, what is the corresponding y-coordinate on the curve y = ln(x)?

• ln(4)

• ln(1)

• ln(2)

• ln(3)

How do you find the y-coordinate when x = 2 + h on the curve y = ln(x)?

• ln(2h)

• ln(2 + h)

• ln(h)

• ln(2)

Tags

CCSS.8.EE.B.5

What is the formula for the slope of a secant line?

• Sum of y-coordinates divided by sum of x-coordinates

• Change in x over change in y

• Product of x and y coordinates

• Change in y over change in x

What is the change in y when moving from x = 2 to x = 2 + h on the curve y = ln(x)?

• ln(2) - ln(h)

• ln(h) - ln(2)

• ln(2 + h) + ln(2)

• ln(2 + h) - ln(2)

Tags

CCSS.HSF-LE.A.1B

What is the change in x when moving from x = 2 to x = 2 + h?

• h

• 2

• 2h

• 2 + h

Tags

CCSS.HSF-IF.C.7E

How does the graph of y = ln(x) generally look?

• A straight line

• A parabola

• An exponential curve

• A logarithmic curve

What is the significance of the points (2, ln(2)) and (2 + h, ln(2 + h)) on the graph?

• They are the points where the curve intersects the x-axis

• They are the maximum points of the curve

• They are the minimum points of the curve

• They are the endpoints of the secant line

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

What does the slope of the secant line represent in this context?

• The maximum value of x

• The minimum value of y

• The average value of y

• The rate of change of y with respect to x

What happens to the slope of the secant line as h approaches zero?

• It becomes infinite

• It approaches the slope of the tangent line

• It becomes undefined

• It becomes zero