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:
From the graph, I can see two points on the line:
- One point is
- Another point is
Now, let's calculate the gradient:
So, the gradient of the blue line is .
Do you want more details or have any questions? Here are 5 related questions to deepen your understanding:
- How does the slope of a line affect its direction?
- What is the gradient of a horizontal line?
- How would the gradient change if the points on the line were swapped?
- Can two different lines have the same gradient? If yes, what does that imply?
- 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
-
Suitable Grade Level
Grades 8-10