Math Problem Statement

what is the gradient

Solution

The gradient (or slope) of a line on a graph is calculated using the formula:

Gradient=Change in yChange in x=y2y1x2x1\text{Gradient} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{y_2 - y_1}{x_2 - x_1}

From the graph you provided, the line passes through the points (0,4)(0, 4) and (4,4)(4, -4).

Let's calculate the gradient:

  1. The change in yy (Δy\Delta y) is y2y1=44=8y_2 - y_1 = -4 - 4 = -8.
  2. The change in xx (Δx\Delta x) is x2x1=40=4x_2 - x_1 = 4 - 0 = 4.

So the gradient is:

Gradient=84=2\text{Gradient} = \frac{-8}{4} = -2

The gradient of the line is 2-2.

Would you like more details or have any questions? Here are some related topics you might find helpful:

  1. What is the significance of the gradient in real-world scenarios?
  2. How do you interpret a negative gradient?
  3. What are the different ways to find the equation of a line?
  4. How do you calculate the gradient if the line is horizontal?
  5. How can the gradient be used to determine the steepness of a line?
  6. What is the relationship between the gradient and the angle of inclination of a line?
  7. How does changing the points on the line affect the gradient?
  8. How would you find the gradient of a curve at a specific point?

Tip: Remember that a negative gradient means the line is sloping downwards from left to right on the graph.

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Math Problem Analysis

Mathematical Concepts

Geometry
Analytic Geometry
Gradient (Slope)

Formulas

Gradient formula: (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 7-9