Understanding Slope and Rate of Change

The video tutorial explains the concept of slope, which is the rise over run, and how it relates to lines and curves. It distinguishes between positive and negative slopes, providing examples for each. The tutorial also covers the rate of change in curves, showing how to calculate it using two points. The video aims to help students understand how to determine the slope of a line or curve and its significance.

What is the primary difference between slope and rate of change?

• Both are associated with curves.

• Both are associated with lines.

• Slope is associated with lines, while rate of change is with curves.

• Slope is associated with curves, while rate of change is with lines.

How do you determine the slope of a line?

• By counting the number of points on the line.

• By counting the total length of the line.

• By counting the rise over the run.

• By counting the run over the rise.

If a line has a rise of 3 and a run of 2, what is its slope?

• 1/2

• 3/2

• 2/3

• 2/1

What does a negative slope indicate about the direction of a line?

• The line slopes downward from left to right.

• The line slopes upward from left to right.

• The line is vertical.

• The line is horizontal.

If a line has a rise of 2 and a run of 4, but slopes downward, what is its slope?

• 2

• -1/2

• 1/2

• -2

How do you calculate the rate of change for a curve?

• By finding the slope of the tangent line.

• By measuring the length of the curve.

• By counting the total number of points on the curve.

• By finding the average of all slopes on the curve.

What is the rate of change if the rise is 3 and the run is 2 for a curve?

• 2/3

• 3/2

• 1/2

• 2/1

If a curve has a rate of change of -3/2, what does this indicate?

• The curve is constant.

• The curve is decreasing.

• The curve is oscillating.

• The curve is increasing.