Math Problem Statement

What is the gradient of the blue line?

Solution

To find the gradient (slope) of the blue line from the graph in the image, we need to identify two clear points on the line and use the formula for the gradient:

Gradient=ΔyΔx=y2y1x2x1\text{Gradient} = \frac{{\Delta y}}{{\Delta x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}}

Step-by-step:

  1. Choose two points on the line:

    • One point appears to be at (4,0)(4, 0) (where the line crosses the x-axis).
    • Another point is at (6,5)(6, 5) (where the line crosses the vertical grid).
  2. Apply the formula: Gradient=5064=52=2.5\text{Gradient} = \frac{{5 - 0}}{{6 - 4}} = \frac{5}{2} = 2.5

Final answer:

The gradient of the blue line is 2.52.5.

Let me know if you would like further clarification or details.


Here are five questions that expand on this concept:

  1. What does the gradient of a line represent in real-world applications?
  2. How does changing the slope of a line affect its steepness?
  3. What is the gradient of a horizontal line?
  4. How do you find the gradient if the line is vertical?
  5. Can two non-parallel lines have the same gradient? Why or why not?

Tip: The greater the gradient, the steeper the slope of the line. If the gradient is negative, the line slopes downwards.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slopes of Lines

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-10