Math Problem Statement
What is the rate of change? Use the y-intercept and the highlighted dot.
Solution
To find the rate of change (or slope) from the graph, we will use the two points highlighted: the y-intercept and the other visible point.
Step-by-Step Process:
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Identify the coordinates of the points:
- The y-intercept appears to be at (where the line crosses the y-axis).
- The second highlighted point appears to be at .
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Use the slope formula: Where and are the coordinates of the two points.
Plugging in the values:
Final Answer:
The rate of change (or slope) is .
This means for every unit increase in , decreases by 40 units.
Would you like more details on this calculation or have any questions?
Here are 5 related questions you might explore:
- What is the equation of the line in slope-intercept form?
- How do you interpret a negative rate of change in a real-world scenario?
- How can you calculate the rate of change using different points on the line?
- What does it mean if the rate of change (slope) is zero?
- How would the graph look if the slope were positive?
Tip: When calculating the slope, always ensure you subtract the values in the same order as the values!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope
Formulas
Slope formula: (y2 - y1) / (x2 - x1)
Theorems
Slope-Intercept Form: y = mx + b
Suitable Grade Level
Grades 7-9