Math Problem Statement
what is the gradient
Solution
To find the gradient of the line in the image, we will again use the formula:
Let's identify two points on the line. Based on the image:
- The line passes through the point .
- It also passes through the point .
Now, 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 does a gradient of imply about the steepness of the line?
- How can you use the gradient to write the equation of the line?
- What would the gradient be if the line was vertical?
- How does the gradient relate to the rise and run of a line?
- Can you determine the gradient if only one point is known?
- How would you find the y-intercept using the gradient and a point on the line?
- What happens to the gradient if the line is reflected over the y-axis?
- How can the concept of gradient be applied in real-life situations?
Tip: When the gradient is a fraction less than 1, it indicates that the line is relatively flat, rising slowly as it moves from left to right.
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Math Problem Analysis
Mathematical Concepts
Gradient
Linear Equations
Slope
Formulas
Gradient formula: Gradient = Change in y / Change in x
Theorems
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Suitable Grade Level
Grades 7-9