Math Problem Statement

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What is the gradient of the straight line shown below?

Solution

The gradient (or slope) of a straight line can be calculated using the formula:

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

From the image, we can identify two points on the line:

  • Point 1: (6,6)(-6, -6)
  • Point 2: (6,6)(6, 6)

Now, apply these coordinates to the formula:

Gradient=6(6)6(6)=6+66+6=1212=1\text{Gradient} = \frac{{6 - (-6)}}{{6 - (-6)}} = \frac{{6 + 6}}{{6 + 6}} = \frac{{12}}{{12}} = 1

Thus, the gradient of the straight line is 1.

Would you like more details, or do you have any questions?

Here are 5 related questions to deepen your understanding:

  1. What does the gradient of a line represent in terms of its steepness?
  2. How does the gradient of a horizontal or vertical line differ?
  3. What is the general equation of a line, and how is the gradient used in it?
  4. How would the gradient change if the line were steeper or flatter?
  5. Can you calculate the gradient from any two points on the line?

Tip: The gradient tells you how much the line rises or falls for each unit it moves horizontally.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Linear Equations

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9