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:

  1. The slope mm of the line appears to be negative since the yy-values decrease as the xx-values increase.
  2. The data points suggest that the slope is around 1.9-1.9, since for every unit increase in xx, yy decreases by approximately 1.9 units.
  3. The yy-intercept (the value of yy when x=0x = 0) is around 10, so the intercept is close to +10.

Given these observations, the most appropriate linear model would have a slope of 1.9-1.9 and a yy-intercept of 10, which corresponds to option B: y=1.9x+10.1y = -1.9x + 10.1.

Would you like further details or have any questions about this?

Here are 5 related questions you can explore:

  1. How can you determine the slope of a line from a scatterplot?
  2. What is the significance of the yy-intercept in linear models?
  3. How do you differentiate between positive and negative slopes visually?
  4. How can linear regression be used to find the exact line of best fit?
  5. 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