Slope and Average Rate of Change

The video tutorial explains how the function r(x) represents the radius of a circle for a given area x. It introduces the concept of rate of change, equating it to the slope of a graph. The tutorial guides viewers through calculating the average slope between two points on a curve, using the slope formula. The process involves identifying points, labeling them, and applying the formula to find the rate of change. The final result is an average rate of change of 0.125 foot per square foot.

What does the function r(x) represent in the context of the video?

• The diameter of a circle for a given area x

• The circumference of a circle for a given area x

• The area of a circle for a given radius x

• The radius of a circle for a given area x

What is another term for the average rate of change?

• Slope

• Intercept

• Integral

• Derivative

Why is the slope not the same everywhere on the curve?

• Because the curve is a circle

• Because the curve is a straight line

• Because the curve is not linear

• Because the curve is a parabola

What are the coordinates of the first point identified on the graph?

• (7, 1.5)

• (7, 1)

• (3, 1.5)

• (3, 1)

What are the coordinates of the second point identified on the graph?

• (7, 1.5)

• (7, 1)

• (3, 1.5)

• (3, 1)

What is the formula for calculating the slope?

• (x2 - x1) / (y2 - y1)

• (y1 - y2) / (x1 - x2)

• (y2 - y1) / (x2 - x1)

• (x1 - x2) / (y1 - y2)

What is the value of y2 in the slope calculation?

• 7

• 3

• 1

• 1.5

What is the value of y1 in the slope calculation?

• 1

• 1.5

• 3

• 7

What is the value of x2 in the slope calculation?

• 1

• 1.5

• 3

• 7

What is the value of x1 in the slope calculation?

• 1

• 7

• 1.5

• 3