Math Problem Statement
What is the gradient of the line shown below? Give your answer as an integer or as a fraction in its simplest form.
Solution
To find the gradient (slope) of the line, we use the formula:
From the graph, we can identify two points on the line to calculate the change in and .
- Point 1: (where the line crosses the y-axis)
- Point 2:
Now, calculate the changes:
Thus, the gradient is:
So, the gradient of the line is 2.
Would you like more details or have any questions? Here are five related questions to expand on this concept:
- What does the gradient represent in terms of real-world applications?
- How would the equation of the line look in slope-intercept form?
- What happens to the gradient if the line becomes horizontal or vertical?
- How can you determine the gradient if the points are not clear from a graph?
- What is the difference between positive and negative gradients?
Tip: The steeper the line, the larger the absolute value of the gradient.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Coordinate Geometry
Formulas
Gradient formula: m = (change in y) / (change in x)
Theorems
Slope of a straight line
Suitable Grade Level
Grades 7-9