Math Problem Statement
Determine the slope of the given line from the graph.
Solution
The graph in the image shows a straight line with a positive slope. The slope () of a line is calculated using the formula:
To determine the slope:
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Select two clear points on the line where it crosses the grid intersections. For example:
- Point 1:
- Point 2:
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Compute the changes in and :
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Substitute into the slope formula:
Thus, the slope of the line is:
Would you like further details or clarification on this? Here are some related questions to explore further:
- What does the slope of a line represent geometrically and practically?
- How does the slope affect the steepness of a line?
- How can you identify if a line has a positive or negative slope from a graph?
- What are the slope-intercept and point-slope forms of the equation of a line?
- How can slope calculations be extended to real-world applications?
Tip: Always double-check that your selected points align exactly with grid intersections to avoid errors when calculating the slope.
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Math Problem Analysis
Mathematical Concepts
Slope of a Line
Linear Algebra
Coordinate Geometry
Formulas
m = Δy / Δx
Theorems
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Suitable Grade Level
Grades 7-8