Math Problem Statement

Work out the gradient of the line on the graph below. Give any decimal answers to 1 d.p.

Solution

To find the gradient (or slope) of the line shown in the graph, we need to use the formula:

Gradient=Change in yChange in x\text{Gradient} = \frac{\text{Change in } y}{\text{Change in } x}

Looking at the graph, we can choose two points on the line and find the difference in their yy and xx values.

  1. The line appears to pass through the points (0, 0) and (10, 50).

    • At (0, 0), x=0x = 0 and y=0y = 0.
    • At (10, 50), x=10x = 10 and y=50y = 50.
  2. Now, calculate the change in yy and xx:

    • Change in yy = 500=5050 - 0 = 50
    • Change in xx = 100=1010 - 0 = 10
  3. Substitute these values into the gradient formula:

Gradient=5010=5.0\text{Gradient} = \frac{50}{10} = 5.0

So, the gradient of the line is 5.0 to one decimal place.

Would you like more details or have any questions?

Here are some related questions you might find helpful:

  1. What does a gradient represent on a graph?
  2. How can we find gradients of lines that are not passing through the origin?
  3. How is the gradient affected if the line slopes downward?
  4. What are the units of the gradient in real-life applications?
  5. How does changing the scale of a graph affect the visual appearance of the gradient?

Tip: When calculating gradients, always ensure the points chosen are accurately read from the graph to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry

Formulas

Gradient formula: (Change in y) / (Change in x)

Theorems

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Suitable Grade Level

Grades 7-9