Math Problem Statement
Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?
Solution
The scatterplot shows a clear downward trend, indicating a negative slope for the linear model. To find the most appropriate equation:
- The slope of the line appears to be negative since the -values decrease as the -values increase.
- The data points suggest that the slope is around , since for every unit increase in , decreases by approximately 1.9 units.
- The -intercept (the value of when ) is around 10, so the intercept is close to +10.
Given these observations, the most appropriate linear model would have a slope of and a -intercept of 10, which corresponds to option B: .
Would you like further details or have any questions about this?
Here are 5 related questions you can explore:
- How can you determine the slope of a line from a scatterplot?
- What is the significance of the -intercept in linear models?
- How do you differentiate between positive and negative slopes visually?
- How can linear regression be used to find the exact line of best fit?
- What role does the correlation coefficient play in determining linearity?
Tip: Always check if the data points suggest a linear trend before applying a linear model.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Scatterplots
Slope-Intercept Form
Formulas
y = mx + b (Slope-Intercept Form)
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Line of Best Fit
Suitable Grade Level
Grades 9-10