Math Problem Statement

What is the gradient of the blue line?

Solution

The image shows a graph with a blue line, and the question asks for the gradient (slope) of that line. To calculate the gradient of a line, we use 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, I can see two points on the line:

  • One point is (5,3)(-5, 3)
  • Another point is (5,2)(5, -2)

Now, let's calculate the gradient:

Gradient=235(5)=55+5=510=12\text{Gradient} = \frac{{-2 - 3}}{{5 - (-5)}} = \frac{{-5}}{{5 + 5}} = \frac{{-5}}{{10}} = -\frac{1}{2}

So, the gradient of the blue line is 12-\frac{1}{2}.

Do you want more details or have any questions? Here are 5 related questions to deepen your understanding:

  1. How does the slope of a line affect its direction?
  2. What is the gradient of a horizontal line?
  3. How would the gradient change if the points on the line were swapped?
  4. Can two different lines have the same gradient? If yes, what does that imply?
  5. How do you find the y-intercept using the gradient and one point on the line?

Tip: The gradient gives an indication of the steepness and direction of the line—negative gradients slope downwards from left to right.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slope of a Line
Linear Equations

Formulas

Gradient (Slope) = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 8-10