Slope of a line secant to a curve | Taking derivatives | Differential Calculus | Khan Academy

TL;DR

Slope is the rate of change of a line, indicating the inclination of the line. We can calculate the slope of a line using two points. In calculus, we can approximate the rate of change of a curve using the average rate of change over an interval.

Transcript

So let's review the idea of slope, which you might remember from your algebra classes. The slope is just the rate of change of a line. Or the rate of change of y, with respect to x, as we go along a line. And you could also view it as a measure of the inclination of a line. So the more incline the line is, the more positive of a slope it would have... Read More

Key Insights

• 🫥 Slope is the rate of change of a line and indicates the inclination of the line.
• 🫥 Two points on a line can be used to calculate the slope.
• ☠️ In calculus, we approximate the rate of change of a curve using the average rate of change over an interval.

Questions & Answers

Q: What does slope represent in a line?

Slope represents the rate of change of the line or the inclination of the line. A positive slope indicates an increasing line, while a negative slope indicates a decreasing line.

Q: How can we calculate the slope of a line?

We can calculate the slope of a line using two points on the line. The slope is the change in y divided by the change in x between the two points.

Q: Can the slope of a line change?

No, the slope of a line is constant for any two points on the line. It represents the rate of change of y with respect to x.

Q: How is the rate of change of a curve estimated in calculus?

In calculus, we can estimate the rate of change of a curve by calculating the average rate of change over an interval. This is done by finding the difference in y divided by the difference in x between two points on the curve.

Summary & Key Takeaways

• Slope is the rate of change of a line or the inclination of the line.

• The slope of a line can be calculated using two points on the line.

• In calculus, we can estimate the rate of change of a curve by calculating the average rate of change over an interval.