Math Problem Statement
what is the gradient
Solution
The gradient (or slope) of a line on a graph is calculated using the formula:
From the graph you provided, the line passes through the points and .
Let's calculate the gradient:
- The change in () is .
- The change in () is .
So the gradient is:
The gradient of the line is .
Would you like more details or have any questions? Here are some related topics you might find helpful:
- What is the significance of the gradient in real-world scenarios?
- How do you interpret a negative gradient?
- What are the different ways to find the equation of a line?
- How do you calculate the gradient if the line is horizontal?
- How can the gradient be used to determine the steepness of a line?
- What is the relationship between the gradient and the angle of inclination of a line?
- How does changing the points on the line affect the gradient?
- How would you find the gradient of a curve at a specific point?
Tip: Remember that a negative gradient means the line is sloping downwards from left to right on the graph.
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Math Problem Analysis
Mathematical Concepts
Geometry
Analytic Geometry
Gradient (Slope)
Formulas
Gradient formula: (y2 - y1) / (x2 - x1)
Theorems
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Suitable Grade Level
Grades 7-9