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Sreeshan · 2024-03-07T13:18:20.180Z

What it Represents: • The gradient tells you how much the y-value of the function (represented by the graph) changes for a given change in the x-value. • A positive gradient indicates that the line or curve slants upwards as you move from left to right on the graph. The y-value increases as the x-value increases. • A negative gradient signifies a downward slope. The y-value decreases as the x-value increases. • A zero gradient corresponds to a horizontal line. The y-value remains constant regardless of the change in the x-value. Calculating Gradient: For a straight line, the gradient can be calculated using the following formula: Gradient = (Change in y-value) / (Change in x-value) This essentially boils down to the difference between the y-coordinates of two points on the line divided by the difference between their x-coordinates. Importance of Gradient: The gradient holds immense significance in understanding the behavior of the function represented by the graph. Here's why: • Rate of Change: It signifies the rate of change of the function's output (y-value) concerning its input (x-value). A steeper slope indicates a faster rate of change. • Real-World Applications: Gradient finds applications in various fields. For example, in economics, it can represent the rate of change of price concerning quantity. In physics, it can depict the velocity (rate of change of position) of an object. Beyond Straight Lines: While the concept of gradient is straightforward for straight lines, things get a bit more nuanced for curves. Here, the gradient applies to a specific point on the curve. We can imagine a tangent line at that point, which is a straight line that just touches the curve at that specific point. The gradient of the curve at that point is then the gradient of the tangent line.

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Sreeshan

Mar 07

Gradient in graphs

in Sreeshan

What it Represents:

The gradient tells you how much the y-value of the function (represented by the graph) changes for a given change in the x-value.
A positive gradient indicates that the line or curve slants upwards as you move from left to right on the graph. The y-value increases as the x-value increases.
A negative gradient signifies a downward slope. The y-value decreases as the x-value increases.
A zero gradient corresponds to a horizontal line. The y-value remains constant regardless of the change in the x-value.

Calculating Gradient:

Importance of Gradient:

Beyond Straight Lines:

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